Adding and Subtracting Functions
Procedure —
To Evaluate the Sum or Difference of Functions
Step 1 Find (f + g)(x) or (f - g)(x).
Step 2 Use x = a to find (f + g)(a) or (f - g)(a).
Example 1
Given f(x) = x2 - 5x and g(x) = 8x - 10, find (f + g)(x) when x = 4.
That is, find (f + g)(4).
Solution
| Step 1 |
Find (f + g)(x).
Substitute for f(x) and g(x).
Simplify.
So, (f + g)(x) = x2 + 3x - 10. |
(f + g)(x) |
= f(x) + g(x)
= (x2 - 5x) + (8x - 10)
= x2 + 3x - 10 |
| Step 2 |
Use x = 4 to find (f + g)(4).
Substitute 4 for x.
Simplify.
Add and subtract. |
(f + g)(x)
(f + g)(4) |
= x2 + 3x - 10
= (4)2 + 3(4) - 10
= 16 + 12 + 10
= 18 |
So, (f + g)(4) = 18.
Example 2
Given f(x) = 8x - 9 and g(x) = 3x2 + 13, find (f - g)(x) when x =
-5.
That is, find (f - g)(-5).
Solution
| Step 1 |
Find (f - g)(x).
Substitute for f(x) and g(x).
Remove parentheses.
Combine like terms.
So, (f - g)(x) = -3x2
+ 8x - 22.
|
(f - g)(x)
(f - g)(x) |
= f(x)
- g(x)
= (8x - 9)
- (3x2 + 13)
= 8x - 9
- 3x2 - 13
= -3x2 + 8x
- 22 |
| Step 2 |
Use x = -5 to find (f
- g)(-5).
Substitute -5 for x.
Simplify.
Subtract. |
(f - g)(-5) |
= -3(-5)2
+ 8(-5) -
22
= -75 - 40
- 22
= -137 |
|