Answer:
[tex]f(x) = 3x^2[/tex] and [tex]g(x) = x + 2[/tex]
Step-by-step explanation:
Given
[tex]h(x) = 3(x+2)^2[/tex]
[tex]h(x) = (fog)(x)[/tex]
Required
Find possible expressions for f(x) and g(x)
[tex]h(x) = (fog)(x)[/tex]
This can be rewritten as:
[tex]h(x) = f(g(x))[/tex]
Recall that [tex]h(x) = 3(x+2)^2[/tex]
So;
[tex]h(x) = f(g(x)) = 3(x+2)^2[/tex]
[tex]f(g(x)) = 3(x+2)^2[/tex]
By comparison, the expression in bracket represents g(x);
Hence;
[tex]g(x) = x + 2[/tex]
Replace g(x) with x
[tex]f(x) = 3(x)^2[/tex]
[tex]f(x) = 3x^2[/tex]
Hence, the possible expressions of f(x) and g(x) are:
[tex]f(x) = 3x^2[/tex] and [tex]g(x) = x + 2[/tex]
