# How do you evaluate sec(sec^-1(-1))?

Oct 17, 2016

$\sec \left({\sec}^{-} 1 \left(- 1\right)\right) = - 1$

#### Explanation:

For any function and its inverse:

$f \left({f}^{-} 1 \left(x\right)\right) = x$

This is half of the definition of the inverse; the other half is:

${f}^{-} 1 \left(f \left(x\right)\right) = x$