Composition of Functions with a third variable

**KeizerSoze** · December 14th 2011, 08:57 PM

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.

**FernandoRevilla** · December 14th 2011, 09:13 PM

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 $a$ .

**HallsofIvy** · December 15th 2011, 04:40 PM

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?

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