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JEE Main Math Class 11 Relations and Functions Part 2 Questions
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© examsnet.com
Question : 33
Total: 95
Let
f
:
R
⟶
R
and
g
:
R
⟶
R
be defined as
f
(
x
)
=
{
log
e
x
,
x
>
0
e
−
x
,
x
≤
0
.
and
g
(
x
)
=
{
x
,
x
≥
0
e
x
,
x
<
0
.
Then, gof :
R
⟶
R
is :
[1-Feb-2024 Shift 1]
one-one but not onto
neither one-one nor onto
onto but not one-one
both one-one and onto
Validate
Solution:
👈: Video Solution
g
(
f
(
x
)
)
=
{
f
(
x
)
f
(
x
)
≥
0
e
f
(
x
)
f
(
x
)
<
0
.
g
(
f
(
x
)
)
=
{
e
−
x
(
−
∞
,
0
]
e
ln
x
(
0
,
1
)
ln
x
[
1
,
∞
)
.
Graph of
g
(
f
(
x
)
)
g
(
f
(
x
)
)
⇒
Many one into
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