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Let’s check out your problem:
Find the inverse function of the function
f
(
x
)
=
2
x
+
7
f(x)=2 x+7
f
(
x
)
=
2
x
+
7
.
\newline
f
−
1
(
x
)
=
x
−
2
7
f^{-1}(x)=\frac{x-2}{7}
f
−
1
(
x
)
=
7
x
−
2
\newline
f
−
1
(
x
)
=
x
−
7
2
f^{-1}(x)=\frac{x-7}{2}
f
−
1
(
x
)
=
2
x
−
7
\newline
f
−
1
(
x
)
=
x
+
7
2
f^{-1}(x)=\frac{x+7}{2}
f
−
1
(
x
)
=
2
x
+
7
\newline
f
−
1
(
x
)
=
x
+
2
7
f^{-1}(x)=\frac{x+2}{7}
f
−
1
(
x
)
=
7
x
+
2
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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
+
7
f(x)=2 x+7
f
(
x
)
=
2
x
+
7
.
\newline
f
−
1
(
x
)
=
x
−
2
7
f^{-1}(x)=\frac{x-2}{7}
f
−
1
(
x
)
=
7
x
−
2
\newline
f
−
1
(
x
)
=
x
−
7
2
f^{-1}(x)=\frac{x-7}{2}
f
−
1
(
x
)
=
2
x
−
7
\newline
f
−
1
(
x
)
=
x
+
7
2
f^{-1}(x)=\frac{x+7}{2}
f
−
1
(
x
)
=
2
x
+
7
\newline
f
−
1
(
x
)
=
x
+
2
7
f^{-1}(x)=\frac{x+2}{7}
f
−
1
(
x
)
=
7
x
+
2
Subtract
7
7
7
:
Subtract
7
7
7
from both sides of the equation to isolate the term with
y
y
y
on one side:
\newline
x
−
7
=
2
y
x - 7 = 2y
x
−
7
=
2
y
Divide by
2
2
2
:
Divide both sides of the equation by
2
2
2
to solve for
y
y
y
:
y
=
x
−
7
2
y = \frac{x - 7}{2}
y
=
2
x
−
7
Write Inverse Function:
Now that we have solved for
y
y
y
, we can write the inverse function. The inverse function, denoted as
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
, is:
\newline
f
−
1
(
x
)
=
x
−
7
2
f^{-1}(x) = \frac{x - 7}{2}
f
−
1
(
x
)
=
2
x
−
7
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