Question

Given that f(x) = −x + 4 and g(x) = −2x − 3, solve for f(g(x)) when x = 2.

Answer 1

f(g(x)) is a "composite function." Can you define what that means? Once you understand this concept, the actual algebra and arithmetic are relatively simple.

Answer 2

I don't really remember but know it

Answer 3

Could you possibly look it up? And then write it down, for later reference and practice?

Answer 4

yes

Answer 5

So, what have you learned by looking up "composite function" ?

Answer 6

x is a placeholder and there's domain and range.

Answer 7

I see that g(x) is the INPUT to function f(x), in f(g(x)).

Write out f(x).

Replace every instance of x with empty parentheses: f( ) = -( ) + 4

Write function g(x) = -2x -3 inside those empty parentheses: g(x) in the left set of empty parentheses, -2x-3 in the right set.

Simplify the resulting expression.

Answer 8

f(x)=-2(3)+4

Answer 9

f( ) = -( ) + 4 has 2 sets of empty parentheses. Write g(x) inside the left set and write -2x-3 inside the other set. This will give you an expression for the composite function f(g(x)). Simplify the right side.