What is the inverse of the function f(x) = x^4 + 12?

To find the inverse of the function f(x) = x⁴ + 12, we first need to express y in terms of x:

Let y = x⁴ + 12. To find the inverse, we switch x and y:

x = y⁴ + 12

Next, we solve for y:

1. Subtract 12 from both sides:

x – 12 = y⁴

2. Now, take the fourth root of both sides:

y = (x – 12)^1/4

Thus, the inverse function is:

f^-1(x) = (x – 12)^1/4

To summarize, the inverse of the function f(x) = x⁴ + 12 is f^-1(x) = (x – 12)^1/4. This means that if you take a value, plug it into the original function, and then take that result and plug it into the inverse function, you will get back to your original input.