AP EAMCET · Maths · Functions
Let \(\mathrm{f}(\mathrm{x})=\sqrt{\frac{x+1}{x+3}}\) and \(\mathrm{g}(\mathrm{x})=\sqrt{\frac{2-x}{x+3}}\) be two real valued functions. Then the domain of \(f / g\) is
- A \((-\infty,-3) \cup[-1, \infty)\)
- B \([-1,2)\)
- C \((-3,2)\)
- D \((-\infty,-3) \cup[2, \infty)\)
Answer & Solution
Correct Answer
(B) \([-1,2)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\sqrt{\frac{x+1}{x-3}}\) and \(g(x)=\sqrt{\frac{2-x}{x+3}}\) Domain for \(\mathrm{f} / \mathrm{g}\) \(\frac{x+1}{x+3} \geq 0 \frac{+-+}{-\infty-3-1}\) \(x \in\left(-{ }^{\circ},-3\right) \cup\left[-1,{ }^{\circ}\right)\) ........(i)…
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 difference between the focal distances of any point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) is 6 . If \((\sqrt{13}, k)\) is an end point of a latus rectum of this hyperbola, then \(\mathrm{k}=\)AP EAMCET 2023 Hard
- The plane passing through \((2,1,-3)\) and perpendicular to \(3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) contains the pointsAP EAMCET 2021 Medium
- \(f(x)=\frac{x}{e^x-1}+\frac{x}{2}+2 \cos ^3 \frac{x}{2}\) on \(R-\{0\}\) isAP EAMCET 2019 Easy
- If, for \(a \neq 0, x=a(1-\sin t), y=a(t+\cos t)\), then \(\frac{d^2 y}{d x^2}=\)AP EAMCET 2017 Easy
- Suppose the tangents drawn to the circle \(x^2+y^2-6 x-4 y-11=0\) from \(P(1,8)\) touch the circle at \(A\) and \(B\). Then the centre of the circle passing through \(P\), \(\mathrm{A}\) and \(\mathrm{B}\) isAP EAMCET 2022 Easy
- The remainder when the polynomial \(2 x^5-3 x^4+5 x^3-3 x^2+7 x-9\) is divided by \(x^2-x-3\) isAP EAMCET 2022 Easy
More PYQs from AP EAMCET
- In each of the following options, a function and an interval are given. Choose the option containing the function and the interval for which Lagrange's mean value theorem is not applicableAP EAMCET 2024 Easy
- If is a tangent drawn to the curve at where are constants, thenAP EAMCET 2019 Easy
- The standard Gibb's energy \(\left(\Delta G^{\circ}\right)\) for the following reaction is
\(\begin{aligned} & A(s)+B^{2+}(a q) \rightleftharpoons A^{2+}(a q)+B(s), \\ & K_C=10^{12} \text { at } 25^{\circ} \mathrm{C}\left(K_C=\text { equilibrium constant }\right)\end{aligned}\)AP EAMCET 2022 Medium - \(\lim _{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{2^2}{n^2}\right) \ldots\left(1+\frac{n^2}{n^2}\right)\right]^{\frac{1}{n}}=\)AP EAMCET 2018 Hard
- If the distance between the foci of a hyperbola \(H\) is 26 and distance between its directrices is \(\frac{50}{13}\) then the eccentricity of the conjugate hyperbola of the hyperbola \(H\) isAP EAMCET 2025 Medium
- If the function \(f(x)=a x^3+b x^2+26 x-24\) satisfies the conditions of Rolle's theorem in \([2,4]\) and \(f^{\prime}\left(3+\frac{1}{\sqrt{3}}\right)=0\), then the value of \(a b\) is equal toAP EAMCET 2021 Hard