TS EAMCET · Maths · Functions
The function \(f: R \rightarrow R\) is defined by \(f(x)=3^{-x}\). Observe the following statements of it I. \(f\) is one-one II. \(f\) is onto III. \(f\) is a decreasing function Out of these, true statement are
- A Only I, II
- B Only II,III
- C Only I,III
- D I,II,III
Answer & Solution
Correct Answer
(A) Only I, II
Step-by-step Solution
Detailed explanation
Since, \(f: R \rightarrow R\) such that \(f(x)=3^{-x}\). Let \(y_1\) and \(y_2\) be two elements of \(f(x)\) such that \[ \begin{aligned} & y_1=y_2 \\ & \Rightarrow \quad 3^{-x_1}=3^{-x_2} \Rightarrow x_1=x_2 \\ & \end{aligned} \] Since, if two images are equal, then their…
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
- If the perpendicular distance from the focus of an ellipse \(\frac{x^2}{9}+\frac{y^2}{b^2}=1(b < 3)\) to its corresponding directrix is \(\frac{4}{\sqrt{5}}\), then the slope of the tangent to this ellipse drawn at \(\left(\frac{3}{\sqrt{2}}, \frac{b}{\sqrt{2}}\right)\) isTS EAMCET 2025 Medium
- For \(0 < x < 1\), the expansion of \(\left(1+\frac{1}{x}\right)^{\frac{1}{2}}\) isTS EAMCET 2020 Easy
- \(\int \frac{1}{16-7 \sin ^2 x} d x=\)TS EAMCET 2023 Medium
- If \(f(x)=x-\frac{1}{x}, x \neq 0\), then \(3 f(x)=\)TS EAMCET 2020 Easy
- Derivative of \((\sin x) x\) with respect to \(x^{(\sin x)}\) isTS EAMCET 2024 Hard
- If the points \((1,2)\) and \((3,4)\) lie on the same side of the straight line \(3 x-5 y+a=0\), then \(a\) lies in the setTS EAMCET 2013 Medium
More PYQs from TS EAMCET
- The bond angles \(\mathrm{H}-\hat{\mathrm{O}}-\mathrm{N}\) and \(\mathrm{O}-\hat{\mathrm{N}}-\mathrm{O}\) in the planar structure of nitric acid molecule are respectivelyTS EAMCET 2024 Medium
- If \(\alpha\) is the angle between any two diagonals of a cube and \(\beta\) is the angle between a diagonal of a cube and a diagonal of its face, which intersects this diagonal of the cube then \(\cos \alpha+\cos ^2 \beta=\)TS EAMCET 2025 Medium
- The displacement of a particle moving in a straight line is given by the expression \(x=A t^3+B t^2+C t+D\) in metres, where \(t\) is in seconds and \(A, B, C\) and \(D\) are constants. The ratio between the initial acceleration and initial velocity isTS EAMCET 2015 Easy
- The maximum value of the function \(f(x)=3 \sin ^{12} x+\) \(4 \cos ^{16} x\) isTS EAMCET 2024 Medium
- If \(\frac{x+1}{\left(x^2+1\right)(x-1)^2}=\frac{A x+B}{x^2+1}+\frac{C}{x-1}+\frac{D}{(x-1)^2}\), then \(\mathrm{A}+\mathrm{B}+\mathrm{C}+\mathrm{D}=\)TS EAMCET 2023 Medium
- A moving particle collides with a stationary particle of mass times the mass of moving particle, the fraction of its kinetic energy transferred to the stationary particle isTS EAMCET 2022 Medium