Question

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

Explanation:

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

$y = 2x - 10$

Step2: Swap $x$ and $y$

$x = 2y - 10$

Step3: Solve for $y$, isolate $2y$

$2y = x + 10$

Step4: Divide by 2 to solve for $y$

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

Answer:

$h(x) = \frac{1}{2}x + 5$ (the fourth option)