Verify that f has an inverse. Then use the function f and the given real number a to find (f −1)'(a). (Hint: See Example 1. If an answer does not exist, enter DNE.) Function Real Number f(x) = 1 6 (x5 + 8x3) a = 16

In this exercise we have to use the knowledge of inverse function to calculate the equations and functions given, in this way we find that:

A)

B)

Given the function:

We need to find:

A function has its inverse function existing lf and only if the given function

fis one-to-one fuction: The given function:

Derivate the equation we have that:

Since and are always positive, so the function is always monetonic

increasing  and it passed the horizontal line test. Therefore, the function is one to one. Then, since the function, is one-to-one, It has inverse. Using the formula:

Since we want to find :

Let take the inverse of both sides:

Because when we set a function into as inverse function, it gives our original input value as:

See more about inverse function at link

Step-by-step explanation:

Check attachment for solution

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.