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For a given input value
m, the function
f outputs a value
n to satisfy the following equation.

7m+2=6n-5
Write a formula for
f(m) in terms of
m.

f(m)=

For a given input value $m$ , the function $f$ outputs a value $n$ to satisfy the following equation. $\newline$ $7m+2=6n-5$ $\newline$ Write a formula for $f(m)$ in terms of $m$ . $\newline$ $f(m)=$

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Find the inverse of a linear function

Full solution

Q. For a given input value

m

, the function

f

outputs a value

n

to satisfy the following equation.

\newline

7m+2=6n-5

\newline

Write a formula for

f(m)

in terms of

m

.

\newline

f(m)=

Isolate n: Isolate n on one side of the equation $7m+2=6n-5$ . To do this, we will first add $5$ to both sides of the equation to get rid of the $-5$ on the right side. $7m + 2 + 5 = 6n - 5 + 5$ This simplifies to: $7m + 7 = 6n$
Divide and solve for $n$ : Divide both sides of the equation by $6$ to solve for $n$ . $\newline$ $\frac{7m + 7}{6} = \frac{6n}{6}$ $\newline$ This simplifies to: $\newline$ $n = \frac{7m + 7}{6}$
Write function $f(m)$ : Write the function $f(m)$ in terms of $m$ . $\newline$ Since $n$ is the output of the function $f$ for the input $m$ , we can write: $\newline$ $f(m) = \frac{7m + 7}{6}$

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