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Mathematics
Mathematics
Problem
Define
k
(
x
)
=
x
+
1
k(x)=x+1
k
(
x
)
=
x
+
1
for all
x
∈
R
x\in\mathbb R
x
∈
R
,
g
(
x
)
=
1
x
g(x)=\dfrac{1}{x}
g
(
x
)
=
x
1
for
x
≠
0
x\ne 0
x
=
0
, and
f
(
x
)
=
x
2
f(x)=x^{2}
f
(
x
)
=
x
2
for
x
>
0
x>0
x
>
0
. Let
h
=
f
∘
g
∘
k
h=f\circ g\circ k
h
=
f
∘
g
∘
k
. The inverse function
h
−
1
(
x
)
h^{-1}(x)
h
−
1
(
x
)
is a)
−
1
x
+
1
-\dfrac{1}{\sqrt{x}}+1
−
x
1
+
1
b)
x
−
1
\sqrt{x}-1
x
−
1
c)
1
x
−
1
\dfrac{1}{\sqrt{x}}-1
x
1
−
1
d)
1
x
2
−
1
\dfrac{1}{x^{2}}-1
x
2
1
−
1
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