1. EXAMPLE 1
Add and subtract functions
Let f (x) = 4x1/2 and g(x) = –9x1/2. Find the following. a.
f(x) + g(x)
SOLUTION
f (x) + g(x)
= 4x1/2 + (–9x1/2)
= [4 + (–9)]x1/2
= –5x1/2 b.
f(x) – g(x)
SOLUTION
f (x) – g(x)
= 4x1/2 – (–9x1/2)
= [4 – (–9)]x1/2
= 13x1/2

2. EXAMPLE 1
Add and subtract functions c.
the domains of f + g and f – g
SOLUTION
The functions f and g each have the same domain: all nonnegative real numbers. So, the domains of f + g and f – g also consist of all nonnegative real numbers.

3. EXAMPLE 2
Multiply and divide functions
Let f (x) = 6x and g(x) = x3/4. Find the following. a.
f (x) g(x)
SOLUTION
f (x) g(x)
= (6x)(x3/4)
= 6x(1 + 3/4)
= 6x7/4 b.
f (x)
g(x)
SOLUTION
f (x)
g(x) = 6x
x3/4 =
6x(1 – 3/4) =
6x1/4

4. EXAMPLE 2
Multiply and divide functions f c.
the domains of f g
and g
SOLUTION
The domain of f consists of all real numbers, and the domain of g consists of all nonnegative real numbers. So, the domain of f g consists of all nonnegative real numbers. Because g(0) = 0, the domain of is restricted to all positive real numbers. f g

5. EXAMPLE 3
Solve a multi-step problem
Rhinos
For a white rhino, heart rate r (in beats per minute) and life span s (in minutes) are related to body mass m (in kilograms) by these functions:
r(m) =
241m–0.25
s(m) =
( )m0.2
• Find r(m) s(m).
• Explain what this product represents.

6. Solve a multi-step problem
EXAMPLE 3
Solve a multi-step problem
SOLUTION
STEP 1
Find and simplify r(m) s(m).
r(m) s(m) =
241m –0.25 [ ( )m0.2 ]
Write product of r(m) and s(m). =
241( )m(– )
Product of powers property
( )m –0.05 =
Simplify. =
( )m –0.05
Use scientific notation.

7. EXAMPLE 3
Solve a multi-step problem
STEP 2
Interpret r(m) s(m).
Multiplying heart rate by life span gives the total number of heartbeats for a white rhino over its entire lifetime.

8. GUIDED PRACTICE
for Examples 1, 2, and 3
Let f (x) = –2x2/3 and g(x) = 7x2/3. Find the following.
f (x) + g(x)
SOLUTION
f (x) + g(x)
= –2x2/3 + 7x2/3
= (–2 + 7)x2/3
= 5x2/3
f (x) – g(x)
SOLUTION
f (x) – g(x)
= –2x2/3 – 7x2/3
= [–2 + ( –7)]x2/3
= –9x2/3

9. GUIDED PRACTICE
for Examples 1, 2, and 3
the domains of f + g and f – g
SOLUTION
The domains of f and g have the same domain: all non-negative real numbers. So , the domain of f + g and f – g also consist of all non-negative real numbers.

10. GUIDED PRACTICE
for Examples 1, 2, and 3
Let f (x) = 3x and g(x) = x1/5. Find the following.
f (x) g(x)
SOLUTION
f (x) g(x)
= 3x x1/5
= 3(x ) 1 + 1/5
= 3x6/5
f (x)
g(x)
SOLUTION
f (x)
g(x) = 3x
x1/5
= 3(x ) 1 – 1/5
= 3x4/5

11. GUIDED PRACTICE
for Examples 1, 2, and 3 f g
the domains of f g and
The domain of f • g consists of all real numbers.
The domain of consists of all real numbers except x = 0.
SOLUTION f g

12. GUIDED PRACTICE
for Examples 1, 2, and 3
Rhinos
Use the result of Example 3 to find a white rhino’s number of heartbeats over its lifetime if its body mass is kilograms.
about heartbeats
ANSWER