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), we can use a substitution.Let u = x-5. Then, express x in terms of u: 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 the terms:f(u) = 3(u² + 10u + 25) - u - 5 + 1f(u) = 3u² + 30u + 75 - u - 4Combine like terms:f(u) = 3u² + 29u + 71.Finally, replace 'u' with 'x' to get f(x):f(x) = 3x² + 29x + 71.This matches option C.
Hint
Use a substitution. Let the argument of the given function (x-5) be a new variable, say 'u'. Then express 'x' in terms of 'u' and substitute it into the function's definition.