Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
Let $f:[2, \infty) \rightarrow R$ be the function defined $f(x)=x^{2}-4 x+5$, then the ranges of $f$ is
MathematicsInverse Trigonometric FunctionsKCETKCET 2020
Options:
  • A $(-\infty, \infty)$
  • B $[1, \infty)$
  • C $(1, \infty)$
  • D $[5, \infty)$
Solution:
1664 Upvotes Verified Answer
The correct answer is: $[1, \infty)$
We have,
$\begin{aligned}
&f(x)=x^{2}-4 x+5 \\
&f(x)=x^{2}-4 x+4+1 \\
&f(x)=(x-2)^{2}+1
\end{aligned}$
$\therefore$ Range of $f(x)$ is $[1, \infty)$.

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.