Skip to main content
Back to FUNCTIONS

JEE MATHEMATICS MCQ: FUNCTIONS

1 Medium
1 of 1
Analyzing +4 | -1
If the domain of the function f(x)=cos⁡−1x2−x+1sin⁡−1(2x−12)f(x) = \frac{{{{\cos }^{ - 1}}\sqrt {{x^2} - x + 1} }}{{\sqrt {{{\sin }^{ - 1}}\left( {\frac{{2x - 1}}{2}} \right)} }} is the interval (α, β)(\alpha ,\,\beta ), then α+β\alpha + \beta is equal to
View answer and explanation
Correct option: A
32\frac{3}{2}
Option A (32\frac{3}{2}) is correct because finding the domain of the given function involves considering the domains of inverse cosine and inverse sine functions, and their intersection gives the interval (12,1](\frac{1}{2}, 1], so α+β=12+1=32\alpha + \beta = \frac{1}{2} + 1 = \frac{3}{2}.

More Questions from FUNCTIONS

Practice All Chapter MCQs →
If f:(−∞,2]⟶(−∞,4]f:(-\infty, 2] \longrightarrow(-\infty, 4], where f(x)=x(4−x)f(x)=x(4-x), then f−1(x)f^{-1}(x) is given by: If g(f(x))=∣sin⁡x∣g(f(x))=|\sin x| and f(g(x))=(sin⁡x)2f(g(x))=(\sin \sqrt{x})^2, then Let f:(2,  3)→(0,  1)f:\left( {2,\;3} \right) \to \left( {0,\;1} \right) be defined by f(x)=x−[x]f\left( x \right) = x - \left[ x \right], then f−1(x){f^{ - 1}}\left( x \right) equals Let f:R→Rf: R \rightarrow R be defined as f(x)=x4f(x)=x^4, Choose the correct answer. Which of the following functions are odd functions Let f(x)=(x+1)2−1(x≥−1)f(x)=(x+1)^2-1(x \geq-1). Then the set S={x:f(x)=f−1(x)}S=\left\{x: f(x)=f^{-1}(x)\right\} contains
Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →