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

m+1=-2(n+6)
Write a formula for
h(n) in terms of
n.

h(n)=

For a given input value $n$ , the function $h$ outputs a value $m$ to satisfy the following equation. $\newline$ $m+1=-2(n+6)$ $\newline$ Write a formula for $h(n)$ in terms of $n$ . $\newline$ $h(n)=$

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Find the inverse of a linear function

Full solution

Q. For a given input value

n

, the function

h

outputs a value

m

to satisfy the following equation.

\newline

m+1=-2(n+6)

\newline

Write a formula for

h(n)

in terms of

n

.

\newline

h(n)=

Subtracting $1$ to isolate $m$ : We are given the equation $m+$ $1$ = $-2$ (n+ $6$ ) and we need to solve for $m$ in terms of $n$ to find the function $h(n)$ . $\newline$ First, we will subtract $1$ from both sides of the equation to isolate $m$ on one side. $\newline$ Calculation: $m =$ $-2$ (n+ $6$ ) - $1$
Distributing $-2$ across terms: Next, we distribute the $-2$ across the terms inside the parentheses. $\newline$ Calculation: $m = -2n - 12 - 1$
Combining like terms: Now, we combine the like terms $-12$ and $-1$ to simplify the equation further. $\newline$ Calculation: $m = -2n - 13$
Expressing $m$ in terms of $n$ : We have now expressed $m$ in terms of $n$ , which gives us the function $h(n)$ . $\newline$ Final formula: $h(n) =$ $-2$ n - $13$

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