Question Detail
Question
Given the function $f(x-5) = 3x^2 - x + 1$, evaluate $f(x)$.
Correct Answer
Option C is the correct answer.
Detailed Explanation
Let $u = x-5$. Then, we can express $x$ in terms of $u$: $x = u+5$.Substitute $x=u+5$ into the given function expression:$f(u) = 3(u+5)^2 - (u+5) + 1$$f(u) = 3(u^2 + 10u + 25) - u - 5 + 1$$f(u) = 3u^2 + 30u + 75 - u - 4$$f(u) = 3u^2 + 29u + 71$.Replacing $u$ with $x$ to find $f(x)$:$f(x) = 3x^2 + 29x + 71$.Thus, option C is the correct answer.
Hint
Use a substitution to change the argument of the function, e.g., let $u = x-5$.