I saw a burst of blue fire...... Ahem, that's impossible, after all, it's not Gatling.

But Yu Huatian's writing speed is really fast.

Only two or three breaths of effort.

A new math problem has been solved.

[The image of the known function y=f(x) is symmetrical with respect to the straight line y=x of the image of y=2^x.] 】

[g(x) is an odd function, and when x>0, g(x)=f(x)-x, then g(-8)=(???) )。 】

【A：-5； B：-6； 】

【C：5； D：6。 】

This is a multiple-choice question involving functions.

At first glance, it's not that hard.

After all, are there multiple choice questions?

It's easier than short-answer questions, isn't it?

It can be seen that although the mathematics teacher Yu Huatian has considered Lin Bei's ingredients, he is not too out of line.

Instead of using a super puzzle as soon as it came up, I chose a decent multiple-choice question.

But......

This question is decent.

But it is for top students like Zeng Xi.

For ordinary students, it is still a little difficult, and for the former Lin Bei, it is even more difficult.

For example, the current Zhang San and Li Si, Wang Teng and Zhao Dali are all eight eyes and one stunned, and they are sluggish.

Even Yang Juntian frowned slightly.

It's not that he can't, it's that his thinking is not very clear, and it takes some time to calculate.

However......

As soon as Yu Huatian's chalk stopped here, Lin Bei over there said synchronously: "Teacher, answer C." ”

Zhang San and Li Si: "??? ”

Wang Teng Zhao Dali: "??? ”

Yang Juntian Lu is extraordinary: "??? ”

Hearing this, everyone in the class was stunned.

Nani?

Made so quickly?

How can it be?

What a guess, right?

Zhang San, Li Si, Wang Teng and Zhao Dali forget it, anyway, they can't do it for seven days and seven nights.

But Yang Juntian, Lu Ren and Chu Bufan are the top students in the class, especially Lu Ren is also the representative of the mathematics class, and his strength is second only to Zeng Xi's existence, but he hasn't even calculated it in such a short time, and as a result, Lin Bei, who is a student of water, answered in seconds?

If this is answered correctly, then it will really be a hell to meet Lord Yama in broad daylight.

"Poof!"

Almost subconsciously, everyone in the class laughed.

Among them, Yang Juntian and Lu Ren didn't bother to calculate anymore, and directly joked and scolded: "An idiot." ”

As for Zhang San and Li Si, Wang Teng and Zhao Dali, they all closed their eyes and supported their foreheads, worried about Lin Bei!

No doubt.

None of them dared to look at it again.

Especially Wang Fatzi, he whispered anxiously, "Brother Bei, my own brother alas, this time it's really the end of the calf, let's beep, it seems to be a bit too much!" ”

Apparently.

None of these people above believe that Lin Bei will get the question right, even if it is impossible to guess blindly.

After all, the probability is so slim.

If this can be done correctly, then Lin Bei doesn't need to study, but can buy lottery tickets directly.

However......

They obviously didn't notice Zeng Xi, the school committee member who was sitting in four seats in the fifth row, his eyes suddenly lit up, and he tilted his head and looked at Lin Bei with a curious expression.

Originally, she was a little skeptical that Lin Bei's volume was full of marks, and there was really plagiarism.

After all, although Lin Bei has a strong talent in Chinese, mathematics is not a language, and it is very difficult to go from 0 to full score.

But now, her suspicions dissipated in an instant.

Don't ask why.

Ask.

That is, Lin Bei's answer is right.

Because she did it too.

Although her speed was a little faster than Lin Bei, it was not much faster, almost front and back.

At the same time.

Yu Huatian, the mathematics teacher on the podium, also had a constricted gaze, and his serious face was full of surprise.

However, he did not immediately admit the correctness of Lin Bei's answer, but asked rhetorically: "Lin Bei, what about the process?" ”

[According to the title......

[The two functions are symmetrical with respect to y=x. 】

[Can be converted from point A(x,y) to point B(y,x).] 】

[It means that the original function y=2^x, which can be directly converted to x=2^y, that is, y=log2x.] 】

[then f(x)=log2x,g(x)=log2x-x.] 】

[Because it is true when x>0, -8 cannot be directly substituted, but it is an odd function. 】

[So g(-8)=-g(8)=-[log2,8-8]=5, the natural answer is option C. 】

Lin Bei didn't even go to the podium to use chalk to calculate, but stood in place and talked for a while.

And then.

And then there became.

Because the answer is already out.

But most of the students below were stunned, obviously not reacting.

As for Zhang San and Li Si, Wang Teng and Zhao Dali and the four of them exclaimed directly: "What are you, what are you talking about?" Book from heaven? Why can't we understand a word? ”

No doubt.

The four of them are real learners.

No matter how detailed Lin Bei is, to them, it is no different from the Book of Heaven.

However, Yang Juntian, Lu Ren and Chu Bufan, who were all scholars, changed their faces immediately.

Especially Yang Juntian.

A bad feeling welled up in his mind.

Just because ......

He suddenly realized that Lin Bei might be right, because the process was very clear.

Although he is not very good at mathematics, his foundation is not bad, how can he not understand it?

And that's exactly what happened.

After Lin Bei finished speaking.

Yu Huatian, the math teacher on the stage, nodded at Lin Bei after pondering for three seconds, "Luo Ji's thinking is very good, and the inverse function is used well, let's look at the next question." ”

Well!

Although I didn't say it directly.

But this meaning is self-evident, Lin Bei is not only right, but also very good.

After all, you don't even need chalk, and you can directly dictate and solve the problem, which is a lot more difficult, isn't it?

See this scene.

Except that Zeng Xi didn't react much.

The people below were so shocked that they almost fell to the ground, and Zhang San, Li Si, Wang Teng, and Zhao Dali were even more excited and almost slapped the table.

Only Yang Juntian, Lu Ren and Chu Bufan, the faces of these scholars are not very good-looking.

Especially Yang Juntian, who was instantly gloomy like water.

A small steel tooth "clicked" again, and it seemed to be broken, but it swallowed directly without spitting it out.

I have to say, this is also a ruthless person!

But the broken steel teeth are just the beginning.

The bigger shock seems to be yet to come.

Saw......

[Knowing the function f(x)=6x^3+9x+1, if f(a)+f(a-1)>2, then the range of a is (???) ）】

This is the second question written by Yu Huatian on the blackboard, which is also a function, which can be filled in the blank or selected.

However, this question is obviously more difficult than the first one.

Don't ask why.

Ask.

That is, there is a hole in the question.

The average person's thinking is to subconsciously substitute a and a-1 into the previous function to calculate the inequality.

But if you really want to do this, you will definitely fall into a pit.

Because once the substitution is solved, the final manifestation is absolutely complicated to make people want to cry.

There are dozens of people in the class.

Except for Zeng Xi's expression, he only picked up the pen for a while and quickly wrote and painted, obviously having ideas.

Everyone else frowned.

Including Yang Juntian, Lu Ren and Chu Bufan, they all felt the difficulty of this question.

Maybe.

It takes a lot of time to get it done.

But they didn't have time to put pen to paper, and even the teacher Yu Huatian on the podium didn't write out the options.

Lin Bei spoke directly, "Teacher, you don't need to write options, this question is not very difficult, it is nothing more than the abstraction of concrete functions, you don't need to study the form of the function f(x), but only need to pay attention to its parity and monotonicity." ”

"Where 6x^3 and 9x are both odd functions, but with an extra constant 1, it is not necessarily."

"So ......"

"You can deform the function and set g(x)."

"Since g(x)=f(x)-1=6x^3+9x, it is an odd function, and if the derivative is made, g'(x)=18x^2+9>0, it means that this function must be monotonically increasing."

"And the 2 on the right in f(a)+f(a-1)>2 is very abrupt, obviously not given for nothing."

"You can change the form."

"Split 2 into 1+1 and put it in front of you."

"Accessible ......"

“f(a)-1+f(a-1)-1＞0。”

"Apparently it becomes g(a)+g(a-1)>0."

"i.e. g(a)>-g(a-1) = g(1-a), and because the function is monotonically increasing, a>1-a."

"In the end, we got 2a>1, a>1/2."