Question Detail
Question
Given the function f(x - 5) = 3x² - x + 1, evaluate f(x)
Correct Answer
Option C is the correct answer.
Detailed Explanation
To find f(x) from f(x-5), let u = x - 5. This implies x = u + 5.Now substitute x = u + 5 into the given expression for f(x-5):f(u) = 3(u + 5)² - (u + 5) + 1Expand (u + 5)²:(u + 5)² = u² + 10u + 25Substitute this back into f(u):f(u) = 3(u² + 10u + 25) - u - 5 + 1f(u) = 3u² + 30u + 75 - u - 5 + 1Combine like terms:f(u) = 3u² + 29u + 71Finally, replace u with x to get f(x):f(x) = 3x² + 29x + 71. This matches option C.
Hint
Let a new variable, say u, be equal to the argument of f on the left side (i.e., u = x - 5). Then express x in terms of u and substitute this into the right side of the equation.