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Find the inverse function of the function
f
(
x
)
=
2
x
−
5
f(x)=2 x-5
f
(
x
)
=
2
x
−
5
.
\newline
f
−
1
(
x
)
=
x
−
2
5
f^{-1}(x)=\frac{x-2}{5}
f
−
1
(
x
)
=
5
x
−
2
\newline
f
−
1
(
x
)
=
x
+
2
5
f^{-1}(x)=\frac{x+2}{5}
f
−
1
(
x
)
=
5
x
+
2
\newline
f
−
1
(
x
)
=
x
−
5
2
f^{-1}(x)=\frac{x-5}{2}
f
−
1
(
x
)
=
2
x
−
5
\newline
f
−
1
(
x
)
=
x
+
5
2
f^{-1}(x)=\frac{x+5}{2}
f
−
1
(
x
)
=
2
x
+
5
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Math Problems
Calculus
Find derivatives of using multiple formulae
Full solution
Q.
Find the inverse function of the function
f
(
x
)
=
2
x
−
5
f(x)=2 x-5
f
(
x
)
=
2
x
−
5
.
\newline
f
−
1
(
x
)
=
x
−
2
5
f^{-1}(x)=\frac{x-2}{5}
f
−
1
(
x
)
=
5
x
−
2
\newline
f
−
1
(
x
)
=
x
+
2
5
f^{-1}(x)=\frac{x+2}{5}
f
−
1
(
x
)
=
5
x
+
2
\newline
f
−
1
(
x
)
=
x
−
5
2
f^{-1}(x)=\frac{x-5}{2}
f
−
1
(
x
)
=
2
x
−
5
\newline
f
−
1
(
x
)
=
x
+
5
2
f^{-1}(x)=\frac{x+5}{2}
f
−
1
(
x
)
=
2
x
+
5
Replace with
y
y
y
:
To find the inverse function, we first replace
f
(
x
)
f(x)
f
(
x
)
with
y
y
y
:
y
=
2
x
−
5
y = 2x - 5
y
=
2
x
−
5
Swap x and y:
Next, we swap x and y to solve for the new y, which will give us the inverse function:
\newline
x
=
2
y
−
5
x = 2y - 5
x
=
2
y
−
5
Solve for new y:
Now, we solve for
y
y
y
by adding
5
5
5
to both sides of the equation:
\newline
x
+
5
=
2
y
x + 5 = 2y
x
+
5
=
2
y
Isolate
y
y
y
:
Finally, we divide both sides by
2
2
2
to isolate
y
y
y
:
y
=
x
+
5
2
y = \frac{x + 5}{2}
y
=
2
x
+
5
This is the inverse function of
f
(
x
)
f(x)
f
(
x
)
.
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Find the derivative of
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Find the derivative of
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\newline
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=
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Find the derivative of
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Find the derivative of
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\newline
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′
(
x
)
=
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f
′
(
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)
=
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