KCET · Maths · Functions
The domain of the function \(\sqrt{\dfrac{x-7}{9-x}}\) is
- A \([7, 9]\)
- B \([7, 9)\)
- C \((7, 9]\)
- D \((7, 9)\)
Answer & Solution
Correct Answer
(B) \([7, 9)\)
Step-by-step Solution
Detailed explanation
For the function to be defined, the expression inside the square root must be non-negative and the denominator must not be zero.
\(\dfrac{x-7}{9-x} \ge 0\) and \(9-x \ne 0\)
Multiplying the numerator and denominator by \(-1\), we get:
\(\dfrac{x-7}{x-9} \le 0\)
The critical points are \(x = 7\) and \(x = 9\).
Using the wavy curve method, the expression \(\dfrac{x-7}{x-9}\) is less than or equal to zero for \(x \in [7, 9]\).
Since the denominator cannot be zero, \(x \ne 9\).
Therefore, the domain of the function is \(x \in [7, 9)\).
Answer: \([7, 9)\)
\(\dfrac{x-7}{9-x} \ge 0\) and \(9-x \ne 0\)
Multiplying the numerator and denominator by \(-1\), we get:
\(\dfrac{x-7}{x-9} \le 0\)
The critical points are \(x = 7\) and \(x = 9\).
Using the wavy curve method, the expression \(\dfrac{x-7}{x-9}\) is less than or equal to zero for \(x \in [7, 9]\).
Since the denominator cannot be zero, \(x \ne 9\).
Therefore, the domain of the function is \(x \in [7, 9)\).
Answer: \([7, 9)\)
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
- How many \( 5 \) digit telephone numbers can be constructed using the digits \( 0 \) to \( 9 \), if each
number starts with \( 67 \) and no digit appears more than once ?KCET 2014 Easy - \( \int \frac{\sin ^{2} x}{1+\cos x} d x \)KCET 2015 Easy
- \(\int \frac{1}{1+3 \sin ^2 x+8 \cos ^2 x} d x\) is equals toKCET 2023 Hard
- In the binomial expansion of \((1+x)^{15}\), the coefficients of \(\mathrm{x}^{\mathrm{r}}\) and \(\mathrm{x}^{\mathrm{r}+3}\) are equal. Then, \(r\) isKCET 2010 Medium
- If \(\sin 2 x=4 \cos x\), then \(x\) is equal toKCET 2012 Easy
- The value of \( \int \frac{e^{6 \log x}-e^{5 \log x}}{e^{4 \log x}-e^{3 \log x}} \mathrm{dx} \) is equal toKCET 2016 Easy
More PYQs from KCET
- A Point object is moving uniformly towards the pole of a concave mirror of focal length \( 25 \mathrm{~cm} \)
along its axis as shown below. The speed of the object is \( 1 \mathrm{~ms}^{-1} \). At \( \mathrm{t}=0 \), the distance of the
object from the mirror is \( 50 \mathrm{~cm} \). The average velocity of theimage formed by the mirror
between time \( t=0 \) and \( t=0.25 \mathrm{~s} \) is
KCET 2019 Easy - Which one of the following is a cationic detergent?KCET 2024 Medium
- Light emitted during the de excitation of electron from \(n=3\) to \(n=2\), when incident on a metal, photoelectrons are just emitted from that metal. In which of the following de excitations photoelectric effect is not possible?KCET 2013 Easy
- Energy of an electron in the second orbit of hydrogen atom is \(E_{2}\). The energy of electron in the third orbit of \(\mathrm{He}^{+}\)will beKCET 2021 Easy
- Of the total incident solar radiation, the percentage of photosynthetically active radiation (PAR) captured by the plants isKCET 2019 Hard
- The value of \(\int \frac{1+x^{4}}{1+x^{6}} d x\) isKCET 2020 Medium