Given that f(x)=x−2/3 Find ff⁻¹(x)

Add $\frac{2}{3}$ to both sides:

$$y = x + \frac{2}{3}$$

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

Now, we find $f(f^{-1}(x))$ by substituting $f^{-1}(x)$ into $f(x)$.

Given $f(x) = x - \frac{2}{3}$, we replace $x$ with $f^{-1}(x)$:

$$f(f^{-1}(x)) = f\left(x + \frac{2}{3}\right)$$ $$f\left(x + \frac{2}{3}\right) = \left(x + \frac{2}{3}\right) - \frac{2}{3}$$ $$f\left(x + \frac{2}{3}\right) = x + \frac{2}{3} - \frac{2}{3}$$ $$f\left(x + \frac{2}{3}\right) = x$$

The result is:

$$ff^{-1}(x) = x$$