Question Detail
Question
Given the functions $f(x) = 3x^2-5$ and $g(x) = 5x-1$, evaluate $f(g(x))$.
Correct Answer
Option A is the correct answer.
Detailed Explanation
To evaluate $f(g(x))$, we substitute $g(x)$ into $f(x)$.$f(g(x)) = f(5x-1)$.Substitute $5x-1$ into the expression for $f(x)$:$f(5x-1) = 3(5x-1)^2 - 5$$= 3((5x)^2 - 2(5x)(1) + 1^2) - 5$$= 3(25x^2 - 10x + 1) - 5$$= 75x^2 - 30x + 3 - 5$$= 75x^2 - 30x - 2$.Thus, option A is the correct answer.
Hint
Substitute the entire function $g(x)$ into $f(x)$ wherever $x$ appears.