G(n)=n+4; f and G (-6)

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:

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x