Question

Let f(x) = 3x²+2, g(x) = 3x - 5. Find the following value or expression.
(fog)(x)

Answer 1

(f∘g)(x) = 27x² -90x +77

Explanation:

The composition of functions (f∘g)(x) is interpreted to mean f(g(x)). The value is found the way any function value is found. The argument is substituted for the variable in the function definition.

Substitution

After substituting g(x) for the argument of f(x), the resulting expression can be simplified.

`(f\circ g)(x) =f(g(x))=f(3x-5)\\\\=3(3x-5)^2+2=3(9x^2-30x+25)+2\\\\\boxed{(f\circ g)(x)=27x^2-90x+77}`