what is the inverse of f:x=x+2/3

June 26, 2026Mathematics

ScanSolve AI Answer

June 26, 2026

Answer

$\textbf{f^{-1}(x) = x - \frac{2}{3}}$

To find the inverse of the function $f(x) = x + \frac{2}{3}$ , follow these steps:

Step 1: Replace $f(x)$ with $y$ . $y = x + \frac{2}{3}$

Step 2: Swap $x$ and $y$ in the equation. $x = y + \frac{2}{3}$

Step 3: Solve the new equation for $y$ . To isolate $y$ , subtract $\frac{2}{3}$ from both sides of the equation. $x - \frac{2}{3} = y$ $y = x - \frac{2}{3}$

Step 4: Replace $y$ with $f^{-1}(x)$ to denote the inverse function. $f^{-1}(x) = x - \frac{2}{3}$

The inverse of $f(x) = x + \frac{2}{3}$ is $\boxed{f^{-1(x) = x - \frac{2}{3}}}$ .

What's next?

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp

More Mathematics Questions

QThe length of an arc is 90cm , the angle subtended at the center of the circle is 240 degree . Calcu…QWhat is formula for finding the length of an arc when giving radio and the angle at the center QA and B shared a profit of 24500 rupees in the proportion 3:7. Each of them gave 2% of his share of…QIs 5 a prime factor QHow do you factor a number into its prime factors

See all Mathematics questions →

Still have questions?

Quick Answer

To find the inverse of the function f(x) = x + (2)/(3), follow these steps: Step 1: Replace f(x) with y.

Asked on June 26, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on June 26, 2026

To find the inverse of the function f(x) = x + (2)/(3), follow these steps: Step 1: Replace f(x) with y. y = x + (2)/(3) Step 2: Swap x and y in the equation. x = y + (2)/(3) Step 3: Solve the new equation for y. To isolate y, subtract (2)/(3) from both sides of the equation. x - (2)/(3) = y y = x - (2)/(3) Step 4: Replace y with f^-1(x) to denote the inverse function. f^-1(x) = x - (2)/(3) The inverse of f(x) = x + (2)/(3) is f^-1(x) = x - (2)/(3). What's next?