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) =
f(x) = Create a free account to view solution
View Solution FreeMore Function Questions
Let f be a real valued function defined by f(x) = , then the range of f(x) is :...Let E = {1, 2, 3, 4} and F = {1, 2}, Then, the number of onto functions from E to F is...The function f: R ~ {0} → R given by f(x) = can be made continuous at x = 0 by defining f(0) as...If f(x) = {x} + { x + 1} + {x + 2} ....... {x + 99}, then the value of [f(√2) is, where {.} denotes fractional par...If F(x) = , then F (x) is: (where { . } denotes fractional part function and [. . ] denotes greatest integer function an...