Question

what is the inverse of the function $f(x) = 2x - 10$?
$\circ$ $h(x) = 2x - 5$
$\circ$ $h(x) = 2x + 5$
$\circ$ $h(x) = \frac{1}{2}x - 5$
$\circ$ $h(x) = \frac{1}{2}x + 5$

Explanation:

Step1: Replace $f(x)$ with $y$

$y = 2x - 10$

Step2: Swap $x$ and $y$

$x = 2y - 10$

Step3: Solve for $y$, add 10 to both sides

$x + 10 = 2y$

Step4: Isolate $y$, divide by 2

$y = \frac{1}{2}x + 5$

Answer:

D. $h(x)=\frac{1}{2}x + 5$