Final answer:
To find the inverse of g(x) = 5x - 2, swap the variables and solve for the other variable. The inverse of g(x) is g^(-1)(x) = (x + 2)/5. The inverse is a function.
Step-by-step explanation:
To find the inverse of a function, you need to swap the variables and solve for the other variable. In this case, we have g(x) = 5x - 2. To find the inverse, we replace g(x) with y and x with y, giving us x = 5y - 2. Now, we can solve this equation for y. Add 2 to both sides and divide by 5 to get y = (x + 2)/5. So, the inverse of g(x) is g^(-1)(x) = (x + 2)/5.
To determine if the inverse is a function, we need to check if each input in the range of g(x) has one and only one corresponding output in the range of g^(-1)(x). Since the equation of the inverse is y = (x + 2)/5, we can see that for every input x, there is exactly one corresponding output y. Therefore, the inverse of g(x) is a function.