SOLUTION: 3. Show that the composition of two linear functions is also a linear function.

Question 127643: 3. Show that the composition of two linear functions is also a linear function.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let

and
and

So

Distribute

Since

, this means that

and

. So this shows us that if f(x) and g(x) are linear, then (f o g)(x) is a linear function.

--------------------------------------------------------------------------------

Now let's verify this statement the other way.

Distribute

Since

, this means that

and

. So this shows us that if f(x) and g(x) are linear, then (g o f)(x) is a linear function.
RELATED QUESTIONS
What similarities and differences do you see between functions and linear equations? Are... (answered by Fombitz)

Express the given function h as a composition of two functions f and g so that... (answered by Boreal)

use the composition of functions to show that f^-1 is as given. f(x)=1/2x-3,... (answered by josgarithmetic)

use the composition of functions to show that f^-1 is as given f(x)=1/2x-3,... (answered by MathLover1)

What is the difference in a linear equation and a linear function? What 'real world'... (answered by rapaljer)

Express the given function h as a composition of two functions f and g so that h(x)=(f o... (answered by MathLover1)

Express the given function h as a composition of two functions f and g so that h(x)=(f o... (answered by josgarithmetic)

1. In the real world, what might be a situation where it is preferable for the data to (answered by stanbon)