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For a given input value
v, the function
f outputs a value
u to satisfy the following equation.

u-5=-4(v-1)
Write a formula for
f(v) in terms of
v.

f(v)=

For a given input value $v$ , the function $f$ outputs a value $u$ to satisfy the following equation. $\newline$ $u-5=-4(v-1)$ $\newline$ Write a formula for $f(v)$ in terms of $v$ . $\newline$ $f(v)=$

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Find the inverse of a linear function

Full solution

Q. For a given input value

v

, the function

f

outputs a value

u

to satisfy the following equation.

\newline

u-5=-4(v-1)

\newline

Write a formula for

f(v)

in terms of

v

.

\newline

f(v)=

Isolate u in the equation: Isolate u in the equation $u-5=-4(v-1)$ . $\newline$ To do this, we will add $5$ to both sides of the equation to get $u$ on one side. $\newline$ $u-5+5 = -4(v-1)+5$ $\newline$ Now simplify the equation. $\newline$ $u = -4(v-1) + 5$
Distribute the $-4$ across the parentheses: Distribute the $-4$ across the parentheses in $-4(v-1)$ . $\newline$ $-4 \times v$ gives us $-4v$ , and $-4 \times -1$ gives us $+4$ . $\newline$ $u = -4v + 4 + 5$
Combine like terms to simplify the equation: Combine like terms $4$ and $5$ to simplify the equation further. $\newline$ $u = -4v + 4 + 5$ $\newline$ $u = -4v + 9$
Write the function $f(v)$ in terms of $v$ : Write the function $f(v)$ in terms of $v$ . $\newline$ Since $u$ is the output of the function $f$ for the input $v$ , we can write $u$ as $f(v)$ . $\newline$ $f(v) =$ $-4$ v + $9$

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