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

3m-5n=11
Write a formula for
g(n) in terms of
n.

g(n)=

For a given input value $n$ , the function $g$ outputs a value $m$ to satisfy the following equation. $\newline$ $3m-5n=11$ $\newline$ Write a formula for $g(n)$ in terms of $n$ . $\newline$ $g(n)=$

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Find the inverse of a linear function

Full solution

Q. For a given input value

n

, the function

g

outputs a value

m

to satisfy the following equation.

\newline

3m-5n=11

\newline

Write a formula for

g(n)

in terms of

n

.

\newline

g(n)=

Equation setup: To find the formula for $g(n)$ , we need to solve the equation $3m - 5n = 11$ for $m$ in terms of $n$ .
Isolating terms with $m$ : Add $5$ n to both sides of the equation to isolate terms with $m$ on one side: $\newline$ $3$ m - $5$ n + $5$ n = $11$ + $5$ n $\newline$ This simplifies to: $\newline$ $3$ m = $11$ + $5$ n
Solving for m: Divide both sides of the equation by $3$ to solve for $m$ : $\newline$ $m = \frac{11 + 5n}{3}$
Writing the function $g(n)$ : Now we can write the function $g(n)$ in terms of $n$ using the expression we found for $m$ : $\newline$ $g(n) = \frac{$ $11$ + $5$ n}{ $3$ }

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