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CBSE Class 12 · 2006 · Relations And Functions XIILong Answer

Find the inverse of the function

f (x) = 4 x - 7

,

x \in R

.

Answer: $f^{- 1} (x) = \frac{x + 7}{4}$

Solution

f

is linear with non-zero slope, hence a bijection on

R

and invertible.
Put

y = f (x)

and solve for

x

.

y = 4 x - 7 \Rightarrow 4 x = y + 7 \Rightarrow x = \frac{y + 7}{4}

Interchange

x

and

y

.

f^{- 1} (x) = \frac{x + 7}{4}

CBSE Class 12 Board · 2006 · Subjective

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