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CBSE Class 12 · 2010 · Relations And Functions XIIVery Short Answer

What is the range of the function

f (x) = \frac{∣ x - 1∣}{( x - 1 )}

?

Answer: Range $= {- 1, 1}$

Solution

The modulus splits into two cases about

x = 1

(where

f

is undefined).

∣ x - 1∣ = {(x - 1), - (x - 1), x > 1 x < 1

For

x > 1 : f (x) = \frac{x - 1}{x - 1} = 1

.
For

x < 1 : f (x) = \frac{- ( x - 1 )}{x - 1} = - 1

.
Only these two values are ever attained.

Range = {- 1, 1}

CBSE Class 12 Board · 2010 · Subjective

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