COMPASSLearning

Talk to us Register Login

CBSE Class 12 · 2008 · Relations And Functions XIIVery Short Answer

If

f (x)

is an invertible function, find the inverse of

f (x) = \frac{3 x - 2}{5}

.

Answer: $f^{- 1} (x) = \frac{5 x + 2}{3}$

Solution

Put

y = f (x)

and solve for

x

in terms of

y

.

y = \frac{3 x - 2}{5} \Rightarrow 5 y = 3 x - 2 \Rightarrow x = \frac{5 y + 2}{3}

Interchanging

x

and

y

gives the inverse rule.

f^{- 1} (x) = \frac{5 x + 2}{3}

CBSE Class 12 Board · 2008 · Subjective

Practise more: all CBSE board PYQs on Relations And Functions XII →

More board questions on Relations And Functions XII

A function $f : R \to R$ defined as $f (x) = x^{2} - 4 x + 5$ is
CBSE 2024View solution →
Students of a school are taken to a railway museum to learn about railways heritage and its history. An exhibit in the museum depicted many rail lines on the track near the railway station. Let $L$ be the set of all rail lines on the railway track and $R$ be the relation on $L$ d …
CBSE 2024View solution →
Let $S$ be the relation defined by $S = {(ℓ_{1}, ℓ_{2}) : ℓ_{1} is perpendicular to ℓ_{2}}$ . Check whether the relation $S$ is symmetric and transitive.
CBSE 2024View solution →
A function $f : [- 4, 4] \to [0, 4]$ is given by $f (x) = 16 - x^{2}$ . Show that $f$ is an onto function but not a one-one function. Further, find all possible values of $α$ for which $f (α) = 7$ .
CBSE 2023View solution →
A relation $R$ in a set $A$ is called ____, if $(a_{1}, a_{2}) \in R$ implies $(a_{2}, a_{1}) \in R$ , for all $a_{1}, a_{2} \in A$ .
CBSE 2020View solution →
Consider a bijective function $f : R_{+} \to (7, \infty)$ given by $f (x) = 16 x^{2} + 24 x + 7$ , where $R_{+}$ is the set of all positive real numbers. Find the inverse function of $f$ .
CBSE 2020View solution →