Question

Anyone?

Let f(x) = x + 2 and g(x) = x2 – 6x + 3. Find g(f(x)).

x2 – 6x + 5

x2 – 5x + 5

x2 – 2x – 5

x2 + 10x + 19

Answer 1

think of it this way

g( f(x) )

^
g is HOSTING f(x), who is inside

Answer 2

so any "x" in the HOST function, will be replace by the GUEST function

Answer 3

wait what? I'm a little bit confused.

Answer 4

$$
f(x) = \color{red}{x+2}\\
g(x) = x^2-6x+3\\
g ( f(x) ) = (\color{red}{x+2})^2-6(\color{red}{x+2})+3
$$

Answer 5

so, expand that, cancel like-terms, and you'd get g(f(x))

Answer 6

Well, f(x) = x + 2, so we plug that in for the x values of g(x), so:

g(f(x)) = (x + 2)^2 - 6(x + 2) + 3
= x^2 + 4x + 4 - 6x - 12 + 3
= x^2 - 2x - 5

Answer 7

Okay thank you. I get it now.

Answer 8

yw