How do you find the inverse of the function f(x) = 5x^4 + 6 when x = 19?

To find the inverse of the function f(x) = 5x^4 + 6 when x = 19, we start by replacing f(x) with y for simplicity:

y = 5x^4 + 6

Next, we need to express x in terms of y. First, we isolate 5x^4:

y - 6 = 5x^4

Now, we divide both sides by 5:

x^4 = (y - 6)/5

To solve for x, we take the fourth root of both sides:

x = ((y - 6)/5)^(1/4)

Now we have the inverse function:

f-1(y) = ((y - 6)/5)^(1/4)

To find the value of the inverse function when x = 19, we set y to 19:

f-1(19) = ((19 - 6)/5)^(1/4)

Simplifying this:

f-1(19) = ((13)/5)^(1/4)

Thus, the value of the inverse function at x = 19 is:

f-1(19) = (13/5)^(1/4)

This gives you the inverse value for the specified x in the function.