Question
Asked Oct 6, 2019
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Composite Functions:

I am wondering how to find f+g, f-g, fg, and f/g?

Problem: f(x)=2x+3, g(x)=x-1 

 

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Expert Answer

Step 1

The problem is concerned with the standard operations on two functions to produce a third function

Step 2

The required combinations are natural extensions of arithmetic operations (addition, etc)

f.g are functions: then
by definition
(ftg)(x) f(x)t g(x);
(fg)x)= f(x)g(x)
f
f(x)
-(x) =
g(x)
help_outline

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f.g are functions: then by definition (ftg)(x) f(x)t g(x); (fg)x)= f(x)g(x) f f(x) -(x) = g(x)

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Step 3

Determining (f+g)(x)...

Given f(x) 2x+3, g(x) = x-1
Then
(f+g (x)= f(x) + g(x)
=2x 3+x-1
3x2
(f-g x) f(x)g(x)
2x 3-x1
=x+4
help_outline

Image Transcriptionclose

Given f(x) 2x+3, g(x) = x-1 Then (f+g (x)= f(x) + g(x) =2x 3+x-1 3x2 (f-g x) f(x)g(x) 2x 3-x1 =x+4

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