Question

identify the inverse of the function $f(x) = \frac{2x-7}{7}$. show all steps. (10 points)○ $\frac{x+5}{2}$○ $\frac{7x-5}{2}$○ $\frac{7x+7}{2}$○ $\frac{2x+5}{7}$

Explanation:

Step1: Set $y = f(x)$

$y = \frac{2x-7}{7}$

Step2: Swap $x$ and $y$

$x = \frac{2y-7}{7}$

Step3: Solve for $y$, multiply by 7

$7x = 2y - 7$

Step4: Isolate term with $y$

$7x + 7 = 2y$

Step5: Solve for $y$

$y = \frac{7x+7}{2}$

Answer:

$\frac{7x+7}{2}$ (corresponding to the third option)