**Functions - Domain and Range; Composition**

**Ex 1** Find the domain and range for
.

**Sol** is defined for or
, and solving this
inequality gives , so the domain is .

Since gives or , the graph of is the top half of the circle ; so the range of f is the set of all y-coordinates of points on this semicircle, which is the interval .

**Ex 2** If and , find and
.

**Sol**
, and
.

**Pr 1** Find the domain and range for .

**Pr 2** Find the domain and range for
.

**Pr 3** Find the domain and range for
.

**Pr 4** Find the domain for
.

**Pr 5** If and
, find
and
.

**Pr 6** If
, find functions f and g (different from h)
such that .

**Pr 7** If , find a function f such that
.

**Pr 8** Find the domain for
.

**Pr 9** Find the domain for
.

Go to Solutions.

Return to Precalculus Home Page.

Lawrence Marx 2002-07-11