TS EAMCET · Maths · Functions
The number of real linear functions \(f(x)\) satisfying \(f(f(x))=x+f(x)\) is
- A 0
- B 4
- C 5
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
Let \(f(x)=a x+b\) Given, \[ \begin{aligned} & f(f(x))=x+f(x) \\ & +b)+b=x+(a x+b) \\ & +a b+b=x+a x+b \end{aligned} \]…
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
- Let \(A_r=\left(x+\frac{1}{x}\right)^3 \cdot\left(x^2+\frac{1}{x^2}\right)^3 \cdot\left(x^3+\frac{1}{x^3}\right)^3 \ldots\). \(\left(x^r+\frac{1}{x^r}\right)^3\). If \(x^2+x+1=0\), then \(\frac{1}{A_3}+\frac{1}{A_6}+\frac{1}{A_9}+\frac{1}{A_{12}}+\ldots . . \infty=\)TS EAMCET 2020 Hard
- \(\int_{-2}^4\left|2-x^2\right| d x=\)TS EAMCET 2025 Medium
- If the interval in which the real valued function \(f(x)=\log \left(\frac{1+x}{1-x}\right)-2 x-\frac{x^3}{1-x^2}\) is decreasing in \((a, b)\), where \(|b-a|\) is maximum, then \(\frac{a}{b}=\)TS EAMCET 2024 Medium
- The radius of a circle \(C_1\) is thrice the radius of another circle \(C_2\) and the centres of \(C_1\) and \(C_2\) are \((1,2)\) and \((3,-2)\) respectively. If they cut each other orthogonally and the radius of the circle \(\mathrm{C}_1\) is 3 r, then the equation of the circle with r as radius and \((1,-2)\) as centre isTS EAMCET 2025 Medium
- Let \(n \in N\) which one of the following is true?TS EAMCET 2018 Easy
- Let \(\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\). If \(\mathbf{c}\) is \(\mathbf{a}\) unit vector such that \(\left[\begin{array}{lll}\mathbf{a} & \mathbf{b} & \mathbf{c}\end{array}\right]\) is maximum, then \(\mathbf{c}=\)TS EAMCET 2020 Easy
More PYQs from TS EAMCET
- A compound microscope has an objective of focal length 1.25 cm and an eyepiece of focal length 5 cm separated by a distance of 7.5 cm. The total magnification produced by the microscope when the final image forms at infinity isTS EAMCET 2025 Medium
- Calculate \(\Delta H\) in \(\mathrm{kJ}\) for the following reaction \[ \mathrm{C}(\mathrm{g})+\mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}_2(\mathrm{~g}) \] Given that, \[ \begin{gathered} \mathrm{H}_2 \mathrm{O}(g)+\mathrm{C}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_2(g) ; \ \Delta H=+131 \mathrm{~kJ} \ \mathrm{CO}(g)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g) ; \ \Delta H=-282 \mathrm{~kJ} \ \mathrm{H}_2(g)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{H}_2 \mathrm{O}(g) ; \ \Delta H=-242 \mathrm{~kJ} \end{gathered} \]TS EAMCET 2008 Easy
- Gelly is a colloidal solution ofTS EAMCET 2012 Easy
- If the system of equations
\((k+1)^3 x+(k+2)^3 y =(k+3)^3\)
\((k+1) x+(k+2) y =k+3\)
\(x+y =1\)
is consistent, then the value of \(k\) isTS EAMCET 2010 Medium - Imagine a person standing on a weighing machine placed inside an elevator. The elevator first accelerates, then moves with a constant velocity and finally decelerates to stop. The maximum and minimum weight recorded are \(80 \mathrm{~kg}\) and \(64 \mathrm{~kg}\), respectively. Find out the true weight of that person considering \(\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)\).TS EAMCET 2021 Easy
- A dielectric circular disc of radíus \(R\) carries a unform surface charge density \(\sigma\). If it rotates about its axis with angular velocity \(\omega\), the magnetic fíeld at the cente of dísc is :TS EAMCET 2019 Hard