# To evaluate f ( − 5 ) , f ( 0 ) , f ( 1 ) , f ( 2 ) , f ( 5 ) valuesby usingthe piecewise function f ( x ) = { 3 x , if x &lt; 0 x + 1 , if 0 ≤ x ≤ 2 ( x − 2 ) 2 , if x &gt; 2

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.1, Problem 30E
To determine

Expert Solution

## Answer to Problem 30E

The required functions of the values are f(5)=15,f(0)=1,f(1)=2,f(2)=3,f(5)=9.

### Explanation of Solution

Given information: consider the piecewise function f(x)={3x,                  if  x<0x+1,               if 0x2(x2)2,         if  x>2

Calculation:

First find the value of f(5)

Since the values of x=5<0

From the above piecewise function,to be taken as

f(x)=3x

f(5)=3(5)f(5)=15

Find the values of f(0),f(1),f(2)

Since the value of x=0,x=1<2,x=2

From the above piecewise function,to be taken as

f(x)=x+1

f(0)=0+1f(0)=1f(1)=1+1f(1)=2f(2)=2+1f(2)=3

Find the value of f(5)

Since the value of x=5>2

From the above piecewise function,to be taken as

f(x)=(x2)2

f(5)=(52)2f(5)=9

Thus, the required function of the values f(5)=15,f(0)=1,f(1)=2,f(2)=3,f(5)=9.

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