Inverse Functions

1. Oct 16, 2010

ghostbuster25

Just want to check that i am doing this question correctly.

f(x) = 2x+5 h(x) = 1/x , x $$\neq$$0

Find the inverse of fh(x)

So first i found the function fh(x)

2*1/x+5

then let y = 2*1/x+5 , x $$\neq$$0

now this is the bit i cant rememeber how to do, when i try and make x the subject do i need to multiply the 2 on the RHS as well as the y on the LHS?

if i multiply the 2 then i end up with f-1(x)=2x+5/x
If i dont i end up with f-1(x) = x+7

2. Oct 16, 2010

cyby

First of all, you do mean f(h(x)), and not fh(x), which to me looks like f(x)*h(x). Under that assumption...

f(h(x)) = 2/x + 5.

So, you have y = 2/x + 5..

To find the inverse, you usually just switch x and y, and solve appropriately.

Can you carry it through from here?

3. Oct 16, 2010

ghostbuster25

I can now thanks :)

I see what you have done but im not sure why 1/x becomes 2/x in this circumstance. Im just trying to understand the mechanics behind it so i can be fully aware. If h(x) was 1/x + 5 would it still be 2/x +5 or 2/x + 10?

your correct in your assumption, my teacher is poor and makes us write it fh(x) instead of f(h(x))

4. Oct 16, 2010

cyby

Whereever you saw x, you needed to replace with 1/x. So all you really have is instead of 2*x + 5, you have 2*(1/x) + 5.

If h(x) = 1/x + 5, and f(x) = 2x + 5 then you will actually have f(h(x)) = 2(1/x + 5) + 5 = 2/x + 15.