Question

If G(F(x))=x^2-3, and G(x)= x-3, find F(3)

Answer 1

somebody help me please!!

Answer 2

well
is just a function composition
$$g(f(x)) = x^2-3\\
g(x)= x-3
$$
so, what's f(x)?
f(x) is whatever was INPUT to make "x" in x-3, to \(x^2-3\)

Answer 3

so
$$
g(x) = x-3\\
f(x) = \color{red}{x^2}\\
g(f(x)) = g(\color{red}{x^2}) = (\color{red}{x^2})-3
$$

Answer 4

so, since your
$$
f(x) = \color{red}{x^2}\\
f(-3) = \color{red}{\square?}^2
$$

Answer 5

ohh is just 3 ahem

Answer 6

so
$$
f(x) = \color{red}{x^2}\\
f(3) = \color{red}{\square?}^2
$$

Answer 7

i'm just not seeing where the x^2 comes from,

Answer 8

g(x) = x-3
g( SOMETHING ) = ( SOMETHING ) -3
g ( f(x) ) = \(x^2 -3\)

Answer 9

oh i see it now

Answer 10

thank you for your help

Answer 11

yw