Question

Let $f(x) = x^2 - 10x$ and $g(x) = e^x + 5$ for $x \in \mathbb{R}$. Then, for all $x$, $g(2x) - (f \circ g)(x) = $}

• A. 30
• B. 20
• C. -30
• D. -20
• E. 15

Hint:

Notice that \( f(x) = (x-5)^2 - 25 \). Substituting \( g(x) = e^x + 5 \) makes \( f(g(x)) = ((e^x+5)-5)^2 - 25 = e^{2x} - 25 \). This "completing the square" method can save significant time.

Answer 1

The Correct Option is A