AP EAMCET · Maths · Functions
If a real valued function \(f\) is defined by \(f(x)=\) \(\frac{a x+\sqrt{a^2-x^2}}{b x}\), then \(f\) is
- A only one-one
- B only onto
- C both one-one and onto
- D neither one-one nor onto
Answer & Solution
Correct Answer
(C) both one-one and onto
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{a x+\sqrt{x^2-a^2}}{b x}\) Then \(f^{\prime}(x)=\frac{-a^2}{b x^2 \sqrt{x^2-a^2}}\) if \(b>0 \Rightarrow f^{\prime}(x) 0 \Rightarrow f(x)\) is increasing \(\Rightarrow f(x)\) is one-one. Now, let \(y=\frac{a x+\sqrt{a^2-x^2}}{b x}\)…
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
- A bag contains 10 similar balls, of which 4 are blue and 6 are red. Three balls are taken out at random from the bag one after the other without replacement. The probabilities that all the three balls drawn are red isAP EAMCET 2023 Easy
- If \(\int e^x\left(\frac{1-\sin x}{1-\cos x}\right) d x=f(x)+\) constant, then \(f(x)\) is equal toAP EAMCET 2008 Medium
- If all the digits in the number 53426 are permuted in all possible ways and are arranged in decreasing order, then the number having rank 89 , isAP EAMCET 2018 Medium
- The locus of the point which is equidistant from the point \((1,1)\) and the line \(\mathrm{x}+\mathrm{y}+1=0\) isAP EAMCET 2023 Easy
- In the interval \(\left(\frac{1}{\mathrm{e}}, \mathrm{e}\right)\), a decreasing function among the following functions isAP EAMCET 2023 Medium
- If the mean deviation about the mean is \(m\) and variance is \(\sigma^2\) for the following data, then \(m+\sigma^2=\)
\begin{array}{|c|c|c|c|c|c|}\hlinex & 1 & 3 & 5 & 7 & 9 \\\hlinef & 4 & 24 & 28 & 16 & 8 \\\hline\end{array}AP EAMCET 2024 Easy
More PYQs from AP EAMCET
- The area (in square units) bounded by \(y=\tan ^{-1} x, y=\cot ^{-1} x\) and the \(Y\)-axis, isAP EAMCET 2019 Medium
- An object of density \(2000 \mathrm{~kg}-\mathrm{m}^{-3}\) is hung from a thin light wire. The fundamental frequency of the transverse waves in the wire is \(200 \mathrm{~Hz}\). If the object is immersed in water such that half of its volume is submerged, then the fundamental frequency of the transverse waves in the wire isAP EAMCET 2018 Hard
- Let \(\alpha_1\) and \(\alpha_2\) be the ordinates of two points \(A\) and \(B\) on a parabola \(y^2=4 a x\) and let \(\alpha_3\) be the ordinate of the point of intersection of its tangents at \(A\) and \(B\). Then, \(\alpha_3-\alpha_2=\)AP EAMCET 2018 Hard
- If and , then impliesAP EAMCET 2021 Medium
- The absolute value of the tangent of the difference of the angles made by the lines \(4 x^2-24 x y+11 y^2=0\) with the \(\mathrm{X}\)-axis isAP EAMCET 2023 Medium
- Bhopal gas tragedy of 1984 was caused byAP EAMCET 2007 Easy