COMEDK202510 May 2025Evening ShiftMathematicsFunctionsActual
If a function f:[2, ) R defined by f(x)=x^2-4 x+5 , then the range of f is
Options
- AR
- B[5, )
- C[2, )
- D[1, )
Correct answer
D. [1, )
Step-by-step solution
The function is given by f(x) = x^2 - 4x + 5 . Completing the square, we have f(x) = (x^2 - 4x + 4) + 1 = (x - 2)^2 + 1 . The domain of the function is [2, ) . For x [2, ) , the term (x - 2) takes values in [0, ) . Consequently, (x - 2)^2 takes values in [0, ) . Adding 1 to both sides, (x - 2)^2 + 1 takes values in [1, ) . Thus, the range of the function f is [1, ) . Answer: [1, )