KCET · Maths · Inverse Trigonometric Functions
Let \(f:[2, \infty) \rightarrow R\) be the function defined \(f(x)=x^{2}-4 x+5\), then the ranges of \(f\) is
- A \((-\infty, \infty)\)
- B \([1, \infty)\)
- C \((1, \infty)\)
- D \([5, \infty)\)
Answer & Solution
Correct Answer
(B) \([1, \infty)\)
Step-by-step Solution
Detailed explanation
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 \([1, \infty)\).
\(\begin{aligned}
&f(x)=x^{2}-4 x+5 \\
&f(x)=x^{2}-4 x+4+1 \\
&f(x)=(x-2)^{2}+1
\end{aligned}\)
\(\therefore\) Range of \(f(x)\) is \([1, \infty)\).
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \( f(x)=x-\frac{1}{x} \) then \( f^{\prime}(-1) \) isKCET 2018 Easy
- The interval in which the function \( f(x)=x^{3}-6 x^{2}+9 x+10 \) is increasing inKCET 2019 Easy
- The value of \(\int e^{\sin x} \sin 2 x d x\) isKCET 2020 Medium
- The distance of the point whose position vector is \((2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})\) from the plane \(\mathbf{r} \cdot(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})=4\) isKCET 2022 Medium
- \(f(x) = (x-1)^2\) for \(x \geq 1\), \(g(x)\) is a function whose graph is the reflection of the graph of \(f(x)\) in the line \(y = x\), then \(g(x)\) isKCET 2026 Easy
- The integrating factor of the differential equation \( \left(2 x+3 y^{2}\right) d y=y d x(y>0) \) isKCET 2019 Easy
More PYQs from KCET
- What is the increasing order of acidic strength among the following?
(i) p-methoxy phenol
(ii) p-methyl phenol
(iii) p-nitro phenolKCET 2018 Hard - When red blood corpuscles containing both A and B antigens are mixed with your blood serum, they agglutinate. Hence your blood group is __________ type.KCET 2010 Hard
- Silencing of a specific mRNA translation could be achieved throughKCET 2018 Medium
- Which of the following amino acids is coded by single codon?KCET 2019 Medium
- The value of \( \lim _{x \rightarrow 0} \frac{[x]}{x} \) isKCET 2018 Easy
- Arrange the following in the increasing order of their basic strengths \(\mathrm{CH}_{3} \mathrm{NH}_{2},\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}\), \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}, \mathrm{NH}_{3}\)KCET 2009 Easy