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CBSE Class 12 · 2011 · Relations And Functions XIILong Answer

Let

f : R \to R

be defined as

f (x) = 10 x + 7

. Find the function

g : R \to R

such that

g o f = f o g = I_{R}

.

Answer: $g (x) = \frac{x - 7}{10}$

Solution

The condition

g o f = f o g = I_{R}

means

g

is the inverse of

f

.
Put

y = f (x) = 10 x + 7

and solve for

x

.

y = 10 x + 7 \Rightarrow x = \frac{y - 7}{10}

So define

g (y) = \frac{y - 7}{10}

, i.e.

g (x) = \frac{x - 7}{10}

Check:

g (f (x)) = \frac{( 10 x + 7 ) - 7}{10} = x

and

f (g (x)) = 10 \cdot \frac{x - 7}{10} + 7 = x

.

g (x) = \frac{x - 7}{10}

CBSE Class 12 Board · 2011 · Subjective

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

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