FunctionHard
Question
If f : R → R
f(x) =
then range of f(x) is
f(x) =
then range of f(x) is
Options
A.(- ∞ , - 1)
B.(- 1, ∞)
C.[2, ∞)
D.(- ∞ , - 3)
Solution
f(x) = 
Let g(x) =
and h(x) = 
. Thus f(x) = h(g(x))
Now, g′(x) =
and h′(x) =
and f′(x) = h′(g(x)) g′(x) < 0
⇒ minimum f(x) =
f(x) = 
= - 1
⇒ maximum h(x) =
f(x) = 
Let g(x) =
and h(x) = . Thus f(x) = h(g(x))Now, g′(x) =
and h′(x) =
and f′(x) = h′(g(x)) g′(x) < 0
⇒ minimum f(x) =
f(x) = = - 1⇒ maximum h(x) =
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