f(x)=5x+2 Inverse mode

Question

f(x)=5x+2        Inverse mode

ash2326 · Answer

Do you want to find the inverse of this function?

anonymous · Answer

Yes

ash2326 · Answer

OK, let $x=f^{-1} (x)$
We must know these relations
$$f^{-1} (f(x))=f(f^{-1} (x))=x$$
Do you get this?

anonymous · Answer

ya

ash2326 · Answer

ok, so let's substitute 
$$x=f^{-1} (x)$$
$$f(f^{-1} (x))=5 \times f^{-1} (x)+2$$
Can you simplify this and find $f^{-1} (x)$ from this?

anonymous · Answer

ow, my brain hurts.

anonymous · Answer

I don't know how to do this.

ash2326 · Answer

Use this here
$$f^{-1} (f(x))=f(f^{-1} (x))=x$$

You have to find $f^{-1} (x)$ from this
$$f(f^{-1} (x))=5 \times f^{-1} (x)+2$$

anonymous · Answer

hmm

anonymous · Answer

Can you teach me?

ash2326 · Answer

Do you know what it means by a function?

ash2326 · Answer

@trumpetmaster7777 I just want to know that if you understand functions, then we can proceed with inverse functions. I'll help you figure out this problem.

anonymous · Answer

@ash2326 You're making it a bit complicated.

Notice that we can re-state $\bf f(x)$ as $\bf y=5x+2$. Now to find the inverse, we switch the place of 'x' and 'y' and we attempt to solve for 'y'. This will be our $\bf f^{-1}(x)$. So let's switch the variables and solve for 'y':$$\bf \implies x=5y+2 \implies x-2=5y \implies f^{-1}(x)=\frac{ x-2 }{ 5 }$$Now to make sure that you got the right answer, you can check that $\bf f(f^{-1}(x))=x$ is actually true by plugging in your inverse function in to the original function.

@trumpetmaster7777

ash2326 · Answer

@genius12 You just handed over the answer. I don't see, how it'll help the user understand.

anonymous · Answer

What I was trying to do was switch the 5x instead of just the x thanks @genius12

anonymous · Answer

@ash2326 Not quite. You see, a lot of our members have seem to developed this idea that giving away the answer is a terrible thing to do. And I agree. However if you note, I didn't just give away the answer. Also by reading through what the OP has posted so far, it makes sense to me to say that the OP has some idea of what he's doing and if given a little "spark", will figure it all out. Now this isn't how it works for every question but it made sense to me to do so for this question.

Basic idea: giving away the answer, if done properly and at the right time, isn't always a bad thing to do.

anonymous · Answer

yw @trumpetmaster7777