COMEDK · Maths · 24. Functions
The domain of the function \(y=\dfrac{1}{\log _{10}(3-x)}+\sqrt{x+7}\) is
- A \((-7,3)\)
- B \((-7,3)-\{0\}\)
- C \([-7,3)-\{2\}\)
- D \([-7,3]-\{1\}\)
Answer & Solution
Correct Answer
(C) \([-7,3)-\{2\}\)
Step-by-step Solution
Detailed explanation
The function is defined if the following conditions are satisfied: 1. The argument of the square root must be non-negative: \(x + 7 \ge 0 \Rightarrow x \ge -7\). 2. The argument of the logarithm must be positive: \(3 - x > 0 \Rightarrow x < 3\). 3. The denominator must not be…
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
- Given \(A = \begin{bmatrix} x & 1 & -2 \end{bmatrix}\) and \(B = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}\). If \(ABA^t = [-20]\) then the value of \(x\) is:COMEDK 2026 Medium
- The number of positive divisors of 4896 isCOMEDK 2012 Easy
- If \(A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 4\end{array}\right], B=\left[\begin{array}{c}7 \\ 16 \\ 22\end{array}\right], X=\left[\begin{array}{c}x \\ y \\ z\end{array}\right]\) and \(A X=B\), then \(z\) is equal toCOMEDK 2012 Easy
- What is the nature of the function \(f(x)=x^3-3 x^2+4 x\) on real numbers?COMEDK 2024 Medium
- In a \(\triangle A B C, \operatorname{cosec} A(\sin B \cos C+\cos B \sin C)=\)COMEDK 2015 Easy
- The function \(y=\dfrac{\log x}{x^3}\) is strictly increasing function forCOMEDK 2025 Medium
More PYQs from COMEDK
- \(\text { The value of } \dfrac{i^{1004}+i^{1006}+i^{1008}+i^{1010}+i^{1012}}{i^{510}+i^{508}+i^{506}+i^{504}+i^{502}} \text { is }\)COMEDK 2024 Easy
- An electric bulb of volume \(300 \mathrm{~cm}^3\) was sealed off during manufacture at a pressure of \(1 \mathrm{~mm}\) of mercury at \(27{ }^{\circ} \mathrm{C}\). The number of air molecules contained in the bulb is,
\((\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\) , \(N_A=6.02 \times 10^{23}\), and \(1 \text{ mm of Hg} = 133.3 \text{ N/m}^2\))COMEDK 2024 Medium - Which of the following is not an antacid?COMEDK 2021 Easy
- The mobility of the charge carriers increases withCOMEDK 2024 Easy
- Which of the following is not true?COMEDK 2023 Easy
- A spherical balloon is being inflated at the rate of \(35 \mathrm{~cm} / \mathrm{min}\). When its radius is \(7 \mathrm{~cm}\), its surface area increases at the rate ofCOMEDK 2014 Easy