Question

Express your answer as a polynomial in standard form.

Given:
f(x) = 3x^2 + 4x – 7
g(x) = 2x - 11
Find: g(f(x))

Answer 1

By substituting f(x) into g(x) and simplifying, we find that g(f(x)) is the polynomial 6x^2 + 8x - 25 in standard form.

Step-by-step explanation:

To express g(f(x)) as a polynomial, we first need to substitute f(x) into g(x). Given f(x) = 3x^2 + 4x – 7 and g(x) = 2x - 11, let's substitute the polynomial for x in g(x).

So, g(f(x)) = 2(3x^2 + 4x - 7) - 11. Simplifying this, we first distribute the 2 to each term in the parentheses: g(f(x)) = 6x^2 + 8x - 14 - 11.

Combining like terms, we have: g(f(x)) = 6x^2 + 8x - 25.

This is our polynomial in standard form. Remember, to check if the answer is reasonable, eliminate terms wherever possible to simplify the algebra.