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

4a+7b=-52
Write a formula for
f(b) in terms of
b.

f(b)=

For a given input value $b$ , the function $f$ outputs a value $a$ to satisfy the following equation. $\newline$ $4a+7b=-52$ $\newline$ Write a formula for $f(b)$ in terms of $b$ . $\newline$ $f(b)=$

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Find the inverse of a linear function

Full solution

Q. For a given input value

b

, the function

f

outputs a value

a

to satisfy the following equation.

\newline

4a+7b=-52

\newline

Write a formula for

f(b)

in terms of

b

.

\newline

f(b)=

Isolate the term with $a$ : Isolate the term with $a$ in the equation $4a + 7b = -52$ . $\newline$ To do this, we subtract $7b$ from both sides of the equation. $\newline$ $4a + 7b - 7b = -52 - 7b$ $\newline$ This simplifies to: $\newline$ $4a = -52 - 7b$
Solve for a: Solve for a by dividing both sides of the equation by $4$ . $\newline$ $a = \frac{{-52 - 7b}}{4}$ $\newline$ This gives us the function $f(b)$ in terms of $b$ .
Simplify the expression for a: Simplify the expression for a, if possible. $\newline$ However, in this case, the expression $(-52 - 7b) / 4$ is already in its simplest form, so no further simplification is needed.

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