# Thread: Composition of Functions with a third variable

1. ## Composition of Functions with a third variable

Given the functions $F(x) = 2x^2 - 7$ and $g(x) = 2x + a$, find all values of a such that the y-intercept of the graph of $(f o g)(x)$ is (0,65)

I understand that (f o g)(x) can be rewritten as f(g(x)) but I have never encountered another variable besides x/y to figure out in this type of question. Can someone help me get started on this one? Thank you.

2. ## Re: Composition of Functions with a third variable

Originally Posted by KeizerSoze
Can someone help me get started on this one? Thank you.
Find $y=(f\circ g)(x)=\ldots$ , for $x=0$ , $y$ must be $0,65$ . Now, you'll have a very simple second degree equation on $a$ .

3. ## Re: Composition of Functions with a third variable

Originally Posted by KeizerSoze
Given the functions $F(x) = 2x^2 - 7$ and $g(x) = 2x + a$, find all values of a such that the y-intercept of the graph of $(f o g)(x)$ is (0,65)

I understand that (f o g)(x) can be rewritten as f(g(x)) but I have never encountered another variable besides x/y to figure out in this type of question. Can someone help me get started on this one? Thank you.
The fact thast you are given "f(x)" and "g(x)" indicates that the only variable in those functions is x. The "a" is a parameter- representing some numerical constant.

$f(g(x))= 2(g(x))^2- 7= 2(2x+a)^2- 7$

Can you finish that? For what value of a do you have f(g(0))= 65?