Answer:
Several functions can work together in one larger function. There are 5 common
operations that can be performed on functions. The four basic operations on functions are adding, subtracting, multiplying, and dividing. The notation for these
functions is as follows.
Addition (f + g)(x) = f(x)+ g(x)
Subtraction (f − g)(x)= f(x) − g(x)
Multiplication (f · g)(x)= f(x)g(x)
Division
f
g
(x) = f(x)
g(x)
When we do one of these four basic operations we can simply evaluate the two
functions at the value and then do the operation with both solutions
Example 1.
f(x) = x
2 − x − 2
g(x)= x +1
find (f + g)( − 3)
Evaluate f and g at − 3
f( − 3) =( − 3)2 − ( − 3) − 3 Evaluate f at − 3
f( − 3) =9 +3 − 3
f( − 3)=9
g( − 3) =( − 3)+1 Evaluate g at − 3
g( − 3) = − 2
f( − 3)+ g( − 3) Add the two functions together
(9)+ ( − 2) Add
7 Our Solution
The process is the same regardless of the operation being performed.
Example 2.
h(x) =2x − 4
k(x) = − 3x + 1
Find (h · k)(5)
Evaluate h and k at 5
h(5)= 2(5) − 4 Evaluate h at 5
h(5) = 10 − 4
Step-by-step explanation:
