Question:

Let f(x)=dfracax+bcx+d, then f∘ f(x)=x, provided that:

Show Hint

A function satisfying f(f(x))=x is called an involution.

Updated On: Mar 19, 2026

\(d=-a\)
\(d=a\)
\(a=b=1\)
a=b=c=d=1

Hide Solution

Verified By Collegedunia

The Correct Option is B

Solution and Explanation

For a fractional linear transformation, f(f(x))=x ⟹ f is self-inverse This condition is satisfied when: a=d

Was this answer helpful?

0

0

Top Questions on composite of functions

If the domain of the function
\[ f(x)=\sin^{-1}\!\left(\frac{5-x}{3+2x}\right)+\frac{1}{\log_e(10-x)} \]
is \( (-\infty,\alpha] \cup [\beta,\gamma) - \{\delta\} \), then \( 6(\alpha+\beta+\gamma+\delta) \) is equal to
- JEE Main - 2026
- Mathematics
- composite of functions
View Solution
Evaluate the expression: \[ f\left(f(f(x))\right) + \left(f(f(x))\right)^2 \quad \text{if} \quad x = 1 \]
- MHT CET - 2025
- Mathematics
- composite of functions
View Solution

Let \(f:\R \rightarrow \R\) and \(g:\R \rightarrow\R\) be functions defined by
\(f(x)=\left\{ \begin{array}{ll} x|x|\sin(\frac{1}{x}), & x\ne0 \\ 0, & x = 0, \end{array} \right.\text{and} \ g(x)=\left\{ \begin{array}{ll} 1-2x, & 0\leq x\leq \frac{1}{2}, \\ 0, & \text{otherwise.} \end{array} \right.\)
Let \(a,b,c,d \in \R\). Define the function \(h:\R\rightarrow\R\) by
\(h(x)=af(x)+b(g(x)+g(\frac{1}{2}-x))+c(x-g(x))+d\ g(x), x\in\R\).
Match each entry in List-I to the correct entry in List-II.

List - I		List - II
(P)	If a = 0, b = 1, c = 0 and d = 0, then	(1)	h is one-one.
(Q)	If a = 1, b = 0, c = 0 and d = 0, then	(2)	h is onto.
(R)	If a = 0, b = 0, c = 1 and d = 0, then	(3)	h is differentiable on \(\R\)
(S)	If a = 0, b = 0, c = 0 and d = 1, then	(4)	the range of h is [0, 1].
		(5)	the range of h is {0, 1}.

The correct option is

JEE Advanced - 2024
Mathematics
composite of functions

View More Questions

Questions Asked in BITSAT exam

View More Questions