For a given input value q, the function f outputs a value r to satisfy the following equation. 11 q-4=3r-6 Write a formula for f(q) in terms of q. f(q)=

Isolate r in equation: We are given the equation 11q - 4 = 3r - 6, and we need to solve for r in terms of q to find the function f(q). First, we will isolate r on one side of the equation.Add 6 to both sides: Add 6 to both sides of the equation to move the constant term from the right side to the left side. 11q - 4 + 6 = 3r - 6 + 6 11q + 2 = 3rDivide by 3 to solve: Now, divide both sides of the equation by 3 to solve for r. (11q + 2) / 3 = 3r / 3 (11q + 2) / 3 = rExpress r in terms: We have now expressed r in terms of q. Since r is the output of the function f for the input q, we can write the function as: f(q) = (11q + 2) / 3

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

11 q-4=3r-6
Write a formula for
f(q) in terms of
q.

f(q)=

For a given input value $q$ , the function $f$ outputs a value $r$ to satisfy the following equation. $\newline$ $11q - 4 = 3r - 6$ $\newline$ Write a formula for $f(q)$ in terms of $q$ . $\newline$ $f(q) =$

View step-by-step help

Home

Math Problems

Algebra 1

Find the inverse of a linear function

Full solution

Q. For a given input value

q

, the function

f

outputs a value

r

to satisfy the following equation.

\newline

11q - 4 = 3r - 6

\newline

Write a formula for

f(q)

in terms of

q

\newline

f(q) =

Isolate $r$ in equation: We are given the equation $11q - 4 = 3r - 6$ , and we need to solve for $r$ in terms of $q$ to find the function $f(q)$ . $\newline$ First, we will isolate $r$ on one side of the equation.
Add $6$ to both sides: Add $6$ to both sides of the equation to move the constant term from the right side to the left side. $\newline$ $11q - 4 + 6 = 3r - 6 + 6$ $\newline$ $11q + 2 = 3r$
Divide by $3$ to solve: Now, divide both sides of the equation by $3$ to solve for $r$ . $(11q + 2) / 3 = 3r / 3$ $(11q + 2) / 3 = r$
Express $r$ in terms: We have now expressed $r$ in terms of $q$ . Since $r$ is the output of the function $f$ for the input $q$ , we can write the function as: $\newline$ $f(q) = \frac{11q + 2}{3}$