Final answer:
To find the inverse of the function h(x) = 2x^5 - 5, swap x and y and solve for y by isolating it on one side of the equation.
Step-by-step explanation:
To find the inverse of the function h(x) = 2x^5 - 5, we need to switch the roles of x and y and solve for y.
Let's start by writing the function as y = 2x^5 - 5.
Next, we swap x and y, giving us x = 2y^5 - 5.
Now we can solve for y. We add 5 to both sides of the equation and then divide by 2. This gives us (x+5)/2 = y^5. To isolate y, we take the fifth root of both sides of the equation, resulting in the inverse function y = ((x+5)/2)^(1/5).
Therefore, the inverse function of h(x) = 2x^5 - 5 is y = ((x+5)/2)^(1/5).