I've tried every way I could think of, but I can't seem to get it right. How do you find the value of g(f(a)) when g(x)= x^2-2 and f(x)=-2x+7 p.s. I know the answer is 4a^2-28a+47..but I want to work through the problem.

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- Jan 16th 2013, 06:30 PMYommzFunctions to find Values
I've tried every way I could think of, but I can't seem to get it right. How do you find the value of g(f(a)) when g(x)= x^2-2 and f(x)=-2x+7 p.s. I know the answer is 4a^2-28a+47..but I want to work through the problem.

- Jan 16th 2013, 06:37 PMabenderRe: Functions to find Values
You offer us and . Did you mean instead of , or vice versa?

- Jan 16th 2013, 06:57 PMYommzRe: Functions to find Values
I fixed it.

- Jan 16th 2013, 07:12 PMMathivadhana99Re: Functions to find Values
g(x) = x^2 – 2

f(x) = -2x+7

First substitute x as a

f(a) = -2a +7

then

g(f(a)) = g(-2a+7)

= (-2a+7)^2 - 2

= 4a^2 - 28a + 47 - Jan 16th 2013, 07:29 PMabenderRe: Functions to find Values
- Jan 16th 2013, 09:46 PMYommzRe: Functions to find Values
What formula did you use to get 4a^ 2-28a+4 from (-2a+7)^ 2-2?

- Jan 16th 2013, 10:19 PMDevenoRe: Functions to find Values

- Jan 17th 2013, 08:44 AMMathivadhana99Re: Functions to find Values
you apply (a+b)^2 formula

(a+b)^2 = a^2 + 2ab + b^2

(-2a+7)^2 -2 = (-2a)^2 + 2(-2a)(7) + (7)^2 - 2

= 4a^2 - 28a + 49 - 2

= 4a^2 - 28a +47 - Jan 17th 2013, 11:27 AMDevenoRe: Functions to find Values
the formula Mathivadhana99 used above is the same one i used:

.

since multiplication of real numbers is commutative:

. so, continuing, we get:

.

this is basic, and just uses the distributive law:

repeatedly.