Question

Let \( f(x) = 6x^2 + 9x + 10 \) and \( g(x) = x^2 - 9x - 9 \). Then the value of \( (f \circ g)(10) \) is

• A. 10
• B. 15
• C. 25
• D. 35
• E. 45

Hint:

When solving function composition, first evaluate the inner function and then substitute the result into the outer function.

Answer 1

The Correct Option is C

First, we need to calculate \( g(10) \): \[ g(x) = x^2 - 9x - 9 \] \[ g(10) = 10^2 - 9(10) - 9 = 100 - 90 - 9 = 1 \] Now, we substitute \( g(10) = 1 \) into \( f(x) \): \[ f(x) = 6x^2 + 9x + 10 \] \[ f(1) = 6(1)^2 + 9(1) + 10 = 6 + 9 + 10 = 25 \] Thus, \( (f \circ g)(10) = 25 \). Therefore, the correct answer is (C).