Question

Find (f•f)(3)

f(x)=x^-x

Answer 1

approximately 1.13

Explanation:

`(f \circ f) = f(f(3))`

Working from the inside...

`f(3) = 3^(-3) =(1)/(3^3) = (1)/(27)`

Now put this result back into f again.

`f((1)/(27))=\left((1)/(27)\right)^(1)/(27)`

Use a calculator to approximate this; the result is 1.13.

Note: an "exact" answer is
`\frac{1}{\sqrt[27]{(1)/(27)}}`.