Operations with Functions


To evaluate a function, plug-in the input for x.
o Example, if f (x) = 5x + 12, then f (4) = 5(4) + 12 = 32.
To operate on functions, plug in the input, then operate.
o Example: Let f(x) = 4x – 5 and g(x) = 3x.

f (x) g(x) 4x53x
 f (x) g(x) 4x53x
 f (x) g(x) (4x5) 3x

f (x)  4x5
g(x) 3x
1. Let f(x) = 4x + 8 and g(x) = 2x − 12.
a.
(f + g)(x)
b. (f − g)(x)
c. (f  g)(x)
d.
 f (x)
 g
 
2. Let f(x) = x − 5 and g(x) = 3x + 9. Perform each function operation.
a. (f + g)(x)
b. (f − g)(x)
c.
 f (x)
 g
 
d.
 g (x)
f
 
3. Let f (x) = 4x − 1 and g(x) = 2x + 3. Perform each function operation.
a. (f + g)(1)
b. (f − g)(5)
c. (g − f)(0)
d. (f • g)(-2)
e.
f (3)
g
g (4)
f
f.
4. Let f (x) = 2x − 5 and g(x) = 4x + 5. Perform each function operation.
a.
(f + g)(-1)
b. (f − g)(10)
c. (g − f)(0.5)
d. (f • g)(7)
e.
f (12)
g
f.
g (15)
f
5. Jill has a regular savings account that has $350 in it. She saves $55 each month in this account.
Jill is also going on tour with her school choir next year. She opens up a new savings account
just for tour. She deposits $25 to start the account and then decides to save $40 each month
from her paycheck into her tour savings account.
a. Write a function to represent the price r (x) for Jill’s regular savings account.
b. Write a function t(x) to represent Jill’s tour savings account.
c. Combine the two functions into one function s(x) r(x) t(x) .
d. Calculate Jill’s total savings after 3 months, 6 months, and 10 months.
(r + t)(3)
(r + t)(6)
(r + t)(10)