9.2.1 Operations with Functions − Worksheet
Example 1: Given f ( x ) = 8 x + 13 and g ( x ) = x 2 − 5 x , find each function. 1. ( f + g )( x ) 2. ( f − g )( x )
3. ( g − f )( x )
Example 2: Given f ( x ) = 2 x 2 + 2 x and g ( x ) = x + 1, find each function. 4. ( fg )( x ) 5. f g x ( )
g f
6.
x ( )
Example 3: Given f ( x ) = 3 x 2 and g ( x ) = 7 − x , find each value. 7. f ( g (5)) 8. g ( f (5))
9. f ( g ( − 2))
Example 4: Given f x x g x x ( ) , ( ) 2 = = −
h x x
2 3 and ( ) ,
1 = + , write each composite function. State the
domain of each. 10. f ( g ( x ))
11. g ( f ( x ))
12. f ( h ( x ))
Example 5: 13. Ron is saving money for college. Each month he deposits 10% of his net income plus an additional $50 into a savings account. His net income, after taxes have been taken out, is 80% of his gross income. a. Write a composite function for the amount that Ron saves each month if his gross income is g .
b. Find the amount that Ron saves in a month when his gross income is $2400.
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