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

3a-5=-4b+1
Write a formula for
h(a) in terms of
a.

h(a)=

For a given input value $a$ , the function $h$ outputs a value $b$ to satisfy the following equation. $\newline$ $3a-5=-4b+1$ $\newline$ Write a formula for $h(a)$ in terms of $a$ . $\newline$ $h(a)=$

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Find the inverse of a linear function

Full solution

Q. For a given input value

a

, the function

h

outputs a value

b

to satisfy the following equation.

\newline

3a-5=-4b+1

\newline

Write a formula for

h(a)

in terms of

a

.

\newline

h(a)=

Isolate terms with $b$ : Add $4b$ to both sides of the equation to isolate terms with $b$ on one side and terms with $a$ on the other side. $\newline$ $3a - 5 + 4b = -4b + 1 + 4b$ $\newline$ This simplifies to: $\newline$ $3a - 5 = 1$
Isolate term with $a$ : Add $5$ to both sides of the equation to isolate the term with $a$ on one side. $\newline$ $3a - 5 + 5 = 1 + 5$ $\newline$ This simplifies to: $\newline$ $3a = 6$
Solve for a: Divide both sides of the equation by $3$ to solve for a. $\newline$ $\frac{3a}{3} = \frac{6}{3}$ $\newline$ This simplifies to: $\newline$ $a = 2$
Solve for b: Step $3$ (Correction): Divide both sides of the equation by $-4$ to solve for b. $3a - 5 = 1$ Now divide by $-4$ $b = \frac{3a - 5}{-4}$
Write the function $h(a)$ : Write the function $h(a)$ in terms of $a$ . $h(a) = \frac{{3a - 5}}{{-4}}$

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