1. ## Determine the following please:

I need to check my answers and don't know the solutions

Let f(x) = 1/x and g(x) = -2x + 5. Determine the following:

a.) f ( g (1) ) = _____________________________
b.) g ( f (1) ) = ____________________________
c.) f ( g (x) ) = ____________________________
d.) g ( f (x) ) = ____________________________
e.) f (2)g(2) = _____________________________

2. I'm not going to work all your problems for you but this is how you do it:
think of f(g(x)) = 1/(-2x + 5) and g(f(x)) = -2(1/x) + 5.

Example:

If f(x) = 2x and g(x) = 3x and h(x) = 4x
then f(g(x)) = 2( 3x ) and f(h(x)) = 2( 4x)
similarly g(f(x)) = 3( 2x ) and g(h(x)) = 3( 4x )
as well as
f(x)g(x) = (2x)(3x)

Whatever is inside the parenthesis is what you place as x for the equation. If f(x) = 2x and they ask you to evaluate f(2) then its just simply 2(2) and g(5) = 3(5).

Hope this helps

3. Thanks, that helps.

So for a. I got 1/3

for b. I get 3

and for e. I get 4 1/2.

Thanks for any feedback.

4. Originally Posted by Humbled_by_math
I need to check my answers and don't know the solutions

Let f(x) = 1/x and g(x) = -2x + 5. Determine the following:

a.) f ( g (1) ) = _____________________________
b.) g ( f (1) ) = ____________________________
c.) f ( g (x) ) = ____________________________
d.) g ( f (x) ) = ____________________________
e.) f (2)g(2) = _____________________________
a) and b) are right. I think you got e) wrong:

e) 1/2(-4 + 5) = -2 + 2 1/2 = 1/2

But I'm sure you can see why.

5. f(2)g(2) = (1/(2))(-2(2) + 5)
= 1/2(-2(2)+5)
= 1/2(-4+5)
= 1/2(1)

= 1/2