Question 15 - Week 5 Practice | Prasnya
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Week 5
Question 15
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Choose the correct option(s) from the following.
Multiple correct
Medium Difficulty
24 March 2024
A
If
g
g
is an even function, then
f
∘
g
f\circ g
is always an even function.
B
If
f
f
is an invertible increasing function, then
f
−
1
f^{-1}
is a decreasing function.
C
The function
f
:
N
→
N
f:\mathbb{N}\to\mathbb{N}
given by
f
(
0
)
=
f
(
1
)
=
f
(
2
)
=
1
f(0)=f(1)=f(2)=1
and
f
(
x
)
=
x
−
1
f(x)=x-1
for
x
≥
3
x\ge3
is onto but not one-one.
D
There exists a function
g
g
which is not one-one and a function
f
f
which is one-one such that
f
∘
g
f\circ g
is one-one.
