Question:
If \(f(x) = \begin{cases} 1 + x & \text{if } 0 \leq x \leq 2 \\ 3 - x & \text{if } 2 < x \leq 3 \end{cases}\) , then \(f[f(x)]\) is
If \(f(x) = \begin{cases} 1 + x & \text{if } 0 \leq x \leq 2 \\ 3 - x & \text{if } 2 < x \leq 3 \end{cases}\) , then \(f[f(x)]\) is
Updated On: Oct 4, 2024
- \(f(f(x)) = \begin{cases} 2 + x & \text{if } 0 \leq x \leq 1 \\ 2 - x & \text{if } 1 < x \leq 2 \\ 4 - x & \text{if } 2 < x \leq 3 \end{cases}\)
- \(f(f(x)) = \begin{cases} 2 + x & \text{if } -1 \leq x \leq 1 \\ 2 - x & \text{if } 1 < x \leq 2 \\ 4 - x & \text{if } 2 < x \leq 3 \end{cases}\)
- \(f[f(x)] = \begin{cases} 2 + x & \text{if } 0 \leq x \leq 1 \\ 2 - x & \text{if } 1 \leq x \leq 2 \\ 4 - x & \text{if } 1 \leq x \leq 3 \\ x & \text{if } 0 \leq x \leq 1 \end{cases}\)
- \(f(f(x)) = \begin{cases} 2 + x & \text{if } -1 \leq x \leq 1 \\ 2 - x & \text{if } 1 < x \leq 2 \\ 4 - x & \text{if } 2 \leq x < 3 \end{cases}\)
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The correct option is (A): \(f(f(x)) = \begin{cases} 2 + x & \text{if } 0 \leq x \leq 1 \\ 2 - x & \text{if } 1 < x \leq 2 \\ 4 - x & \text{if } 2 < x \leq 3 \end{cases}\)
Was this answer helpful?
0
0
Top Questions on Functions
- For any non-zero real number x, let\( f(x) + 2f\left(\frac{1}{x}\right) = 3x.\)Then, the sum of all possible values of x for which f(x) = 3, is
- A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is
- The interval, in which the function \( f(x) = \frac{3}{x} + \frac{x}{3} \) is strictly decreasing, is:
- Let the sum of the maximum and the minimum values of the function \( f(x) = \frac{2x^2 - 3x + 8}{2x^2 + 3x + 8} \) be \( \frac{m}{n} \), where \( \text{gcd}(m, n) = 1 \). Then \( m + n \) is equal to:
- Let \(f(x) = \begin{cases} -a & \text{if } -a \leq x \leq 0, \\ x + a & \text{if } 0<x \leq a \end{cases} \) where \(a>0\) and \(g(x) = (f(|x|) - |f(x)|)/2\). Then the function \(g : [-a, a] \to [-a, a]\) is:
View More Questions
Questions Asked in SRMJEEE exam
Calculate the Reynold’s number for a liquid of density 1 g/cm3, viscosity 8 x 10-4 Pa.s flowing at 0.5 m/s through a pipe of diameter 4 cm?
- SRMJEEE - 2023
- Fluid Mechanics
Which of the following statement is true for aqueous solution of 0.1 M urea, 0.2 M glucose nad 0.3 M sucrose
- SRMJEEE - 2023
- Biomolecules
The molar conductivities at infinite dilution for Na2SO4,K2S04,KCl, HCl and HCOONa at 300K are 260, 308, 150, 426, and 105 S cm2 mol-1, respectively. What will be A+m for formic acid in the same unit?
- SRMJEEE - 2023
- Electrochemistry
Electrophilic halogenation of phenol does not require catalyst because
- SRMJEEE - 2023
- Haloalkanes and Haloarenes
- Which one is the correct expression of electric potential on the axial point of a dipole whose dipole moment is р and length is 2l, at a distance of r?
- SRMJEEE - 2023
- Electrostatics
View More Questions