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For a given input value
x, the function
f outputs a value
y to satisfy the following equation.

y+6=5(x-4)
Write a formula for
f(x) in terms of
x.

f(x)=

For a given input value $x$ , the function $f$ outputs a value $y$ to satisfy the following equation. $\newline$ $y+6=5(x-4)$ $\newline$ Write a formula for $f(x)$ in terms of $x$ . $\newline$ $f(x)=$

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Find the inverse of a linear function

Full solution

Q. For a given input value

x

, the function

f

outputs a value

y

to satisfy the following equation.

\newline

y+6=5(x-4)

\newline

Write a formula for

f(x)

in terms of

x

.

\newline

f(x)=

Given equation: We are given the equation $y+6=5(x-4)$ and we need to solve for $y$ in terms of $x$ to find the function $f(x)$ .
Distributing the $5$ : First, distribute the $5$ on the right side of the equation to both terms inside the parentheses: $5(x)$ and $5(-4)$ . $\newline$ This gives us $y+6 = 5x - 20$ .
Isolating y: Next, we subtract $6$ from both sides of the equation to isolate $y$ on one side. $\newline$ This results in $y = 5x - 20 - 6$ .
Combining constants: Now, we combine the constants on the right side of the equation. $\newline$ This simplifies to $y = 5x - 26$ .
Writing the function: Finally, we write the function $f(x)$ in terms of $x$ using the simplified equation for $y$ . $\newline$ So, $f(x) = 5x - 26$ .

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