Question

find the inverse function of the function $f(x) = \frac{4x}{5}$. answer attempt 1 out of 2 $f^{-1}(x) = -\frac{5x}{4}$ $f^{-1}(x) = \frac{4x}{5}$ $f^{-1}(x) = \frac{5x}{4}$ $f^{-1}(x) = -\frac{4x}{5}$

Explanation:

Step1: Set $y=f(x)$

$y = \frac{4x}{5}$

Step2: Swap $x$ and $y$

$x = \frac{4y}{5}$

Step3: Solve for $y$

Multiply both sides by 5: $5x = 4y$
Divide by 4: $y = \frac{5x}{4}$

Step4: Replace $y$ with $f^{-1}(x)$

$f^{-1}(x) = \frac{5x}{4}$

Answer:

$f^{-1}(x) = \frac{5x}{4}$