First slide

Functions (XII)

Question

Statement-1: f : $R \to R$ is a function defined by f(x) = 5x + 3. If $g = f^{- 1},$ then $g (x) = \frac{x - 3}{5} .$
Statement-2: If $f : A \to B$ is a bijection and $g : B \to A$ is the inverse of $f,$ then $f o g$ is the identity function on A.

Moderate

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C

STATEMENT-1 is True, STATEMENT-2 is False
D

STATEMENT-1 is False, STATEMENT-2 is True

Solution

$Let y = 5 x + 3 \Rightarrow x = \frac{y - 3}{5}$
$\to g (x) = \frac{x - 3}{5}$ is the inverse of f, so statement-1 is True
Statement-2 is false because $g : B \to A a n d f : A \to B \Rightarrow f o g : B \to B a n d g = f^{- 1} \Rightarrow f o g$ is an identity function on B.

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