# Thread: 2 functions F(x) and G(x)

1. ## 2 functions F(x) and G(x)

 Two functions are defined as and

I have been stuck on this question for a long time and I have to find:

and

So can somebody please either give me the results with showing the process or just help me through with a detailed explanation.
I would be very grateful

2. ## Re: 2 functions F(x) and G(x)

Originally Posted by leonm92
 Two functions are defined as and

I have been stuck on this question for a long time and I have to find:

and

So can somebody please either give me the results with showing the process or just help me through with a detailed explanation.
I would be very grateful
Evaluate g at x = -4, then put this value as x in f.

Follow a similar process for the second...

Edit: I think I may have made a mistake. Are you using fg and gf as the multiplication of the two functions or the composition of the two functions? If it's the latter, follow what I did...

3. ## Re: 2 functions F(x) and G(x)

I don't know to be honest but I followed what you said and it worked for both. Could you tell me what to do with please

4. ## Re: 2 functions F(x) and G(x)

Originally Posted by leonm92
I don't know to be honest but I followed what you said and it worked for both. Could you tell me what to do with please
Can you evaluate the inverse function of f? Write it as y = , then swap the x and the y values and transpose.

5. ## Re: 2 functions F(x) and G(x)

I've just been reading over it but I can't get my head around it

6. ## Re: 2 functions F(x) and G(x)

$\displaystyle f(x) = y = \frac{2x+9}{-4x-5}$

swap $\displaystyle x$ and $\displaystyle y$ (because that is what an inverse function does ... )

$\displaystyle x = \frac{2y+9}{-4y-5}$

solve for $\displaystyle y$ ...