Question

If \( f(x) = x + 8 \), and \( g(x) = 2x^2 \), then \( (g \circ f)(x) \) is equal to

• A. \( (2x + 8)^2 \)
• B. \( 2(x + 8)^2 \)
• C. \( 2x^2 + 8 \)
• D. \( 2x^2 + 64 \)
• E. \( 2x^3 + 8x \)

Hint:

To compute \( (g \circ f)(x) \), substitute \( f(x) \) into \( g(x) \).

Answer 1

The Correct Option is B

We are given the functions \( f(x) = x + 8 \) and \( g(x) = 2x^2 \), and we are asked to find \( (g \circ f)(x) \), which means \( g(f(x)) \). 
By the definition of composition of functions, we substitute \( f(x) \) into \( g(x) \). Therefore, we have: \[ (g \circ f)(x) = g(f(x)) = g(x + 8). \] 
Now, substitute \( x + 8 \) into the expression for \( g(x) \): \[ g(x + 8) = 2(x + 8)^2. \] 
Thus, \( (g \circ f)(x) = 2(x + 8)^2 \). 
Thus, the correct answer is \( \boxed{2(x + 8)^2} \), corresponding to option (B).