Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If f : R → R ; f(x) = 
then find the range of f(x).
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(– 1, ∞ )
Sol. f(x) = 
= 
Let g(x) = 
and h(x) = 
. Thus f(x) = h(g(x))
Now, g ′ (x) = 
= 
> 0 and h ′ (x) = 
= 
< 0
and f ′ (x) = h ′ (g(x)) g ′ (x) < 0
⇒ minimum f(x) = 
f(x) = 
= 
= – 1
⇒ maximum h(x) = 
f(x) = 
= 
= 
= ∞ ⇒ Range of f(x) = (– 1, ∞ )
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