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

-2u+6v=9
Write a formula for
h(v) in terms of
v.

h(v)=

For a given input value $v$ , the function $h$ outputs a value $u$ to satisfy the following equation. $\newline$ $-2u + 6v = 9$ $\newline$ Write a formula for $h(v)$ in terms of $v$ . $\newline$ $h(v) =$

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Find the inverse of a linear function

Full solution

Q. For a given input value

v

, the function

h

outputs a value

u

to satisfy the following equation.

\newline

-2u + 6v = 9

\newline

Write a formula for

h(v)

in terms of

v

.

\newline

h(v) =

Isolating terms with v: We are given the equation $-2u + 6v = 9$ and we need to solve for $u$ in terms of $v$ to find the function $h(v)$ . Let's start by adding $2u$ to both sides to isolate the terms with $v$ on one side. $\newline$ $-2u + 6v + 2u = 9 + 2u$ $\newline$ This simplifies to: $\newline$ $6v = 9 + 2u$
Getting constant terms on one side: Next, we subtract $9$ from both sides to get all the constant terms on one side. $\newline$ $6v - 9 = 9 + 2u - 9$ $\newline$ This simplifies to: $\newline$ $6v - 9 = 2u$
Solving for u: Now, we divide both sides by $2$ to solve for $u$ . $\newline$ $\frac{6v - 9}{2} = \frac{2u}{2}$ $\newline$ This simplifies to: $\newline$ $u = \frac{6v - 9}{2}$
Writing the function $h(v)$ : Since $u$ is the output of the function $h$ for the input $v$ , we can write the function as: $\newline$ $h(v) = \frac{{6v - 9}}{{2}}$

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