For a given input value a, the function f outputs a value b to satisfy the following equation. -3a+6b=a+4b Write a formula for f(a) in terms of a. f(a)=

Combine like terms: Combine like terms by moving all terms involving a to one side and all terms involving b to the other side. -3a + 6b = a + 4b Add 3a to both sides and subtract 4b from both sides to isolate the terms with b on one side. -3a + 3a + 6b - 4b = a + 3a + 4b - 4b Simplify the equation. 6b - 4b = 4a 2b = 4aIsolate terms with b: Solve for b in terms of a. Divide both sides of the equation by 2 to solve for b. 2b / 2 = 4a / 2 Simplify the equation. b = 2aSimplify the equation: Write the function f(a) in terms of a. Since b is the output of the function f for the input a, we can write b as f(a). f(a) = 2a

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

-3a+6b=a+4b
Write a formula for
f(a) in terms of
a.

f(a)=

For a given input value $a$ , the function $f$ outputs a value $b$ to satisfy the following equation. $\newline$ $-3a+6b=a+4b$ $\newline$ Write a formula for $f(a)$ in terms of $a$ . $\newline$ $f(a)=$

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Math Problems

Algebra 1

Find the inverse of a linear function

Full solution

Q. For a given input value

a

, the function

f

outputs a value

b

to satisfy the following equation.

\newline

-3a+6b=a+4b

\newline

Write a formula for

f(a)

in terms of

a

\newline

f(a)=

Combine like terms: Combine like terms by moving all terms involving $a$ to one side and all terms involving $b$ to the other side. $\newline$ $-3a + 6b = a + 4b$ $\newline$ Add $3a$ to both sides and subtract $4b$ from both sides to isolate the terms with $b$ on one side. $\newline$ $-3a + 3a + 6b - 4b = a + 3a + 4b - 4b$ $\newline$ Simplify the equation. $\newline$ $6b - 4b = 4a$ $\newline$ $2b = 4a$
Isolate terms with $b$ : Solve for $b$ in terms of $a$ . $\newline$ Divide both sides of the equation by $2$ to solve for $b$ . $\newline$ $\frac{2b}{2} = \frac{4a}{2}$ $\newline$ Simplify the equation. $\newline$ $b = 2a$
Simplify the equation: Write the function $f(a)$ in terms of $a$ . $\newline$ Since $b$ is the output of the function $f$ for the input $a$ , we can write $b$ as $f(a)$ . $\newline$ $f(a) = 2a$