Question

what is the inverse of the function f(x) = 2x - 10?
○ h(x) = 2x - 5
○ h(x) = 2x + 5
○ h(x) = (1/2)x - 5
○ h(x) = (1/2)x + 5

Explanation:

Step1: Replace f(x) with y

We start with the function \( f(x) = 2x - 10 \). To find the inverse, we first replace \( f(x) \) with \( y \), so we have \( y = 2x - 10 \).

Step2: Swap x and y

Next, we swap the roles of \( x \) and \( y \). This gives us \( x = 2y - 10 \).

Step3: Solve for y

Now we solve the equation \( x = 2y - 10 \) for \( y \). First, we add 10 to both sides of the equation: \( x + 10 = 2y \). Then, we divide both sides by 2 to isolate \( y \): \( y=\frac{x + 10}{2}=\frac{1}{2}x+5 \).

Step4: Replace y with \( h(x) \)

Finally, we replace \( y \) with \( h(x) \) (the inverse function notation) to get \( h(x)=\frac{1}{2}x + 5 \).

Answer:

\( h(x)=\frac{1}{2}x + 5 \) (corresponding to the option: \( h(x)=\frac{1}{2}x + 5 \))