Question

Given the functions:

f(x) = 2x - 9 and g(x) = 2x + 4x^2 + 8
Find h(x) = f(2) + g(x).

a) h(x) = x^3 + 3x^2 + 8x + 2
b) h(x) = x^3 + 5x^2 + 80 - 16
c) h(x) = 23 + 3x^2 + 8x + 2
d) h(x) = 23 - 3x^2 - 82 - 2

Answer 1

To find h(x), we need to substitute the given values into the functions and simplify the expression.

Step-by-step explanation:

To find h(x), we need to substitute the given values into the functions and simplify the expression:

Given:

f(x) = 2x - 9

g(x) = 2x + 4x^2 + 8

Substituting x = 2 into f(x):
f(2) = 2(2) - 9 = -5

Substituting g(x) into the expression:
h(x) = -5 + (2x + 4x^2 + 8)

Simplifying h(x):
h(x) = 4x^2 + 2x + 3

Therefore, the answer is h(x) = 4x^2 + 2x + 3 (option c).