Question

Express your answer as a polynomial in standard form.

f(x) = x² + 4x – 1
g(x) = 2x - 7
Find: g(f(x))

Answer 1

To find g(f(x)), substitute the function f(x) = x² + 4x - 1 into g(x). The polynomial in standard form for g(f(x)) is 2x² + 8x - 9.

Step-by-step explanation:

To find g(f(x)), we need to substitute the function f(x) = x² + 4x - 1 into g(x).

So, g(f(x)) = 2(f(x)) - 7.

Substituting f(x) into g(x), we get:

g(f(x)) = 2(x² + 4x - 1) - 7.

Expanding and simplifying, we have:

g(f(x)) = 2x² + 8x - 2 - 7.

Combining like terms, the polynomial in standard form is: g(f(x)) = 2x² + 8x - 9.