Algebra and Trigonometry, 5th Edition

5.1 Inverse Functions

• Determine whether a function is one-to-one, and if it is, find a formula for its inverse.

• Simplify expressions of the type $(f\circ f^{-1})(x)$ and $(f^{-1}\circ f)(x)$.

Inverses

When we go from an output of a function back to its input or inputs, we get an inverse relation. When that relation is a function, we have an inverse function.

Consider the relation h given as follows:

$$h=\{(-8,5),(4,-2),(-7,1),(3.8,6.2)\}.$$

Suppose we interchange the first and second coordinates. The relation we obtain is called the inverse of the relation h and is given as follows:

RELATIONS

REVIEW SECTION 1.2

$$\mathrm{Inverse of}h=\{(5,-8),(-2,4),(1,-7),(6.2,3.8)\}.$$

Inverse Relation

Interchanging the first and second coordinates of each ordered pair in a relation ...