Question 25 - Week 5 Practice | Prasnya
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Week 5
Question 25
00:00
Est. 4 min
Marks:
+4.00
0.00
Define a function
f
(
x
)
=
{
x
2
+
1
,
x
<
1
,
x
3
,
x
≥
1.
f(x)=\begin{cases}x^2+1, & x<1,\\ x^3, & x\ge1.\end{cases}
Which of the following options is/are true?
Multiple correct
Medium Difficulty
06 August 2023
A
f
(
x
)
f(x)
is invertible in its domain.
B
f
(
x
)
f(x)
is invertible when the domain is restricted to
[
1
,
∞
)
[1,\infty)
.
C
f
(
x
)
f(x)
is invertible when the domain is restricted to
[
−
1
,
1
]
[-1,1]
.
D
The inverse of
f
(
x
)
f(x)
when the domain is restricted to
[
1
,
∞
)
[1,\infty)
is
f
−
1
(
x
)
=
x
1
/
3
f^{-1}(x)=x^{1/3}
.
E
The inverse of
f
(
x
)
f(x)
when the domain is restricted to
(
−
∞
,
0
)
(-\infty,0)
is
f
−
1
(
x
)
=
x
−
1
f^{-1}(x)=\sqrt{x-1}
.
