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 (x = u+5).Substitute (x = u+5) into the given expression for (f(x-5)):(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)Now, replace (u) with (x) to find (f(x)):(f(x) = 3x^2 + 29x + 71).
Hint
Use a substitution, let \(u = x-5\), and then express \(x\) in terms of \(u\).