Given F(x) shown below, complete the equation for the inverse of F(x). If necessary, use the slash mark (/) for the division symbol.
F(x)=(2x-3)/5
f^-1(y)=_______

Question

Given F(x) shown below, complete the equation for the inverse of F(x). If necessary, use the slash mark (/) for the division symbol.
F(x)=(2x-3)/5
f^-1(y)=_______

anonymous · Answer

help please

hero · Answer

I showed you the steps already.

anonymous · Answer

i know but this is kind of hard for me

hero · Answer

The first step is y = F(x), right?

anonymous · Answer

yes Sr.

hero · Answer

Please, just call me Hero

hero · Answer

If y = F(x), then

$$y = \frac{2x - 3}{5}$$

hero · Answer

The next step is to swap x and y

anonymous · Answer

ok

hero · Answer

Because you're basically taking the graph of the function and flipping it over the axis over the line y = x

$$x = \frac{2y - 3}{5}$$

hero · Answer

That's why you swap x and y. But to complete the process of finding the inverse, you have to isolate y.

hero · Answer

$$5x = 2y - 3$$
$$5x + 3 = 2y$$

$$\frac{5x + 3}{2} = y$$

This gives us the inverse of F(x)

hero · Answer

So we replace y with $F^{-1}(x)$

anonymous · Answer

ok

anonymous · Answer

so it looks somethin like 5x+3/2 right

hero · Answer

(5x + 3)/2

anonymous · Answer

do i have to pur () < this

hero · Answer

Yes, you do

hero · Answer

Otherwise it gets misinterpreted

anonymous · Answer

OMG so i basically got everythin wrongggggg >:|

hero · Answer

Well that depends

hero · Answer

Did you input it like this:

$$\frac{5x + 3}{2}$$

or like this:

5x + 3/2

anonymous · Answer

the sec one

hero · Answer

It should be (5x + 3)/2 if you write it horizontally