AP EAMCET · Maths · Functions
If \(f: R \rightarrow R\) and is defined by \(f(x)=\frac{1}{2-\cos 3 x}\) for each \(x \in R\), then the range of \(f\) is
- A \((1 / 3,1)\)
- B \([1 / 3,1]\)
- C \((1,2)\)
- D \([1,2]\)
Answer & Solution
Correct Answer
(B) \([1 / 3,1]\)
Step-by-step Solution
Detailed explanation
\begin{array}{lrl}\text { Given, } & f(x)= & \frac{1}{2-\cos 3 x} \\ \because & & -1 \leq \cos 3 x \leq 1 \\ \Rightarrow & 1 \leq-\cos 3 x \leq-1 \\ \Rightarrow & 2+1 & \leq 2-\cos 3 x \leq 2-1 \\ \Rightarrow & 3 \leq 2-\cos 3 x \leq 1 \\ \Rightarrow & \frac{1}{3} \leq…
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
- The sum of the solutions in \((0,2 \pi)\) the equation \(\cos x \cos \left(\frac{\pi}{3}-x\right) \cos \left(\frac{\pi}{3}+x\right)=\frac{1}{4}\) isAP EAMCET 2014 Medium
- The function \(f(x)=\left\{\begin{array}{cc}\frac{x-|x|}{x}, & x \neq 0 \\ 2, & x \neq 0\end{array}\right.\)AP EAMCET 2024 Easy
- If the chord through \((1,-2)\) cuts the curve \(3 x^2-y^2-2 x+\) \(4 y=0\) at \(P\) and \(Q\), then the angle subtended by \(P Q\) at the origin isAP EAMCET 2023 Medium
- If \(\frac{a}{a_1}=\frac{b}{b_1}\), then the substitution to be used to solve the differential equation \(\frac{d y}{d x}=\frac{a x+b y+c}{a_1 x+b_1 y+c_1}\) by using separation of variables isAP EAMCET 2022 Easy
- Let be three non zero complex numbers such that . if the determinant , thenAP EAMCET 2021 Easy
- A straight line is equally inclined to all the three coordinate axes. Then, an angle made by the line with the \(y\)-axis isAP EAMCET 2012 Easy
More PYQs from AP EAMCET
- \[
\sqrt{\sin ^4 x+4 \cos ^2 x}-\sqrt{\cos ^4 x+4 \sin ^2 x}=
\]AP EAMCET 2022 Medium - The absolute minimum value of \(x^4-x^2-2 x+5\) isAP EAMCET 2021 Easy
- In which of the following reactions, benzaldehyde is formed from benzoyl chloride and hydrogen in the presence of ?AP EAMCET 2018 Medium
- When \(\mathrm{KI}\) is reacted with \(\mathrm{O}_3\) under aqueous condition the product formed isAP EAMCET 2022 Easy
- Which of the following statements are correct?
i. \(\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-},\left[\mathrm{MnCl}_6\right]^{3-}\) both are paramagnetic
ii. Both \(\left[\mathrm{NiCl}_4\right]^{2-},\left[\mathrm{Ni}(\mathrm{CO})_4\right]\) are tetrahedral and diamagnetic
iii. \(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}\) is inner orbital complex, but \(\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_6\right]^{2+}\) is outer orbital complexAP EAMCET 2023 Medium - Three moles of an ideal monotomic gas performs a cycle \(A B C D A\) as shown in the figure. The temperatures of the gas at the states \(A, B, C\) and \(D\) are \(400 \mathrm{~K}, 800 \mathrm{~K}, 2400 \mathrm{~K}\) and \(1200 \mathrm{~K}\), respectively. The work done by the gas during this cycle is (\(R\) is universal gas constant)
AP EAMCET 2019 Hard