Question

Given the function: g(x) = -1/2x + 3, what is the inverse function of g(x)?

Answer 1

The inverse function of g(x) = -1/2x + 3 is f(x) = -2x + 6.

Step-by-step explanation:

The inverse function of g(x) = -1/2x + 3 can be found by swapping the x and y variables and solving for y. Let's call the inverse function f(x). So we have:

x = -1/2f(x) + 3

To isolate f(x), we can first subtract 3 from both sides:

x - 3 = -1/2f(x)

Then, we can multiply both sides by -2 to get rid of the fraction:

-2(x - 3) = f(x)

Simplifying:

f(x) = -2x + 6

So, the inverse function of g(x) is f(x) = -2x + 6.