Question

If f(x) = 2x – 12 and g(x) = 5x + 8 6. f(x) + g(x)

Answer 1

We will investigate the composition of functions and their applications.

We are given the following two functions:

`\begin{gathered} f\text{ ( x ) = 2x - 12} \\ g\text{ ( x ) = 5x + 8} \end{gathered}`

Composite functions are comprised of two or more functions which are expressed by an mathematical operation or substitution. The possible mathematical operations that can be applied to the functions are as follows:

`\text{Addition, Subtraction, Multiplication, Division}`

The function composition is expressed as follows:

`f\text{ ( x ) + g ( x )}`

We can express the composite function as a singular function by induvidual addition of the comprising functions as follows:

`(f\text{ + g) ( x ) = ( 2x - 12 ) + ( 5x + 8 )}`

A singular composite function is defined as follows:

`\begin{gathered} (f\text{ + g ) ( x ) = ( 5x + 2x ) + ( 8 - 12 )} \\ (f\text{ + g ) ( x ) = 3x - 4} \end{gathered}`

The singular function for composition of functions ( f ( x ) and g ( x ) ) is:

`f\text{ ( x ) + g ( x ) = ( f + g ) ( x ) = 3x - 4}`