If f(x) = 2x - 1 and g(x) = 2x + 1, evaluate f(g(x)) when x = -3

Evaluate f(x) = 2x + 4 for x = 5

This means to substitute 5 for x and simplify. It is recommended that the value being substituted be placed inside parentheses. (This is just to make things easier to look at.)

f(5) = 2(5) + 4 = 14

Adding and Subtracting Functions

To add functions, add their outputs; to subtract functions, subtract their outputs.

Example

Given f(x) = x2 and g(x) = 4x + 1

f(x) + g(x) = x2 + 4x + 1

(f + g)(x) = x2 + 4x + 1

f(x) − g(x) = x2 − (4x + 1) = x2 − 4x − 1   (remember the distributive property)

(f − g)(x) = x2 − 4x − 1

Multiplying a Function by a Constant

To multiply a function by a constant, multiply the output by that constant.

Example

Given f(x) = 4x − 1, find 2f(x).

f(x) = 4x − 1

2f(x) = 2(4x − 1) = 8x − 2

Multiplying a Function by a Function

To multiply a function by another function, multiply the outputs.

Example

Given f(x) = 2x and g(x) = x + 1, find f(x)g(x)

f(x)g(x) = (2x) × (x + 1) = 2x(x + 1)

f(x)g(x) = 2x2 + 2x

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