find the inverse function f(x)=x2-x+1
Answers
Answer:
et
y
=
f
(
x
)
and solve for
x
.
We find that there is no inverse function unless the domain of
f
(
x
)
is restricted.
Explanation:
Suppose
f
(
x
)
=
x
2
−
1
To attempt to find an inverse function, let
y
=
f
(
x
)
and solve for
x
in terms of
y
...
y
=
x
2
−
1
Add
1
to both sides to get:
y
+
1
=
x
2
Transpose and take square root of both sides, allowing for either sign:
x
=
±
√
y
+
1
This does not determine a unique value for
x
in terms of
y
. So there is no inverse function, unless we restrict the domain of
f
(
x
)
.
For example, if we specify an explicit domain
[
0
,
∞
)
for
f
(
x
)
, then
f
−
1
(
y
)
=
√
y
+
1
Alternatively, we might specify an explicit domain
(
−
∞
,
0
]
for
f
(
x
)
, then
f
−
1
(
y
)
=
−
√
y
+
1
Step-by-step explanation: