# That the given function is continuous on its domain and state the domain.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2, Problem 24RE

(a)

To determine

## To find:That the given function is continuous on its domain and state the domain.

Expert Solution

The given function is continuous on its domain (,3][3,) .

### Explanation of Solution

Given information:

The given function is g(x)=x29x22 .

Calculation:

The equation x29 is a polynomial, therefore is continuous on (,) .

And, x is continuous on [0,] .

If g is continuous at a and f is continuous at g(a) , then the composite function fog given by (fog)(x)=f(g(x)) is continuous at a .

The composition x29 is continuous on {x|x290}=(,3][3,) .

1x22 is continuous when x2 and x2 .

If f and g are continuous at a , then f/g is also continuous at a .

The function g(x)=x29x22 is continuous on its domain (,3][3,) .

Therefore, the given function is continuous on its domain (,3][3,) .

(b)

To determine

### To find:That the given function is continuous on its domain and state the domain.

Expert Solution

The given function is continuous on its domain (,) .

### Explanation of Solution

Given information:

The given function is h(x)=xesinx .

Calculation:

x is a polynomial, therefore is continuous on (,) .

And, sinx is a trigonometric function, therefore is continuous on (,) .

And, ex is aexponential function, therefore is continuous on (,) .

If g is continuous at a and f is continuous at g(a) , then the composite function fog given by (fog)(x)=f(g(x)) is continuous at a .

If f and g are continuous at a , then fg is also continuous at a .

The function h(x)=xesinx is continuous on its domain (,) .

Therefore, the given function is continuous on its domain (,) .

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