Let F(x)=3x and g(y)=1y, how do you find each of the compositions and domain and...

Cameron Russell

Cameron Russell

Answered

2022-01-22

Let F(x)=3x and g(y)=1y, how do you find each of the compositions and domain and range?

Answer & Explanation

Appohhl

Appohhl

Expert

2022-01-23Added 11 answers

For: (fg)(x)
h(x)=[3x]x=g(x)=1x=31x=3x
For: (gf)(x)
r(x)=[1x]x=f(x)=3x=13x
Madelyn Townsend

Madelyn Townsend

Expert

2022-01-24Added 13 answers

Required:
Composite functions: a) (fg)(x) and b) (gf)(x)
For: (fg)(x)
Step 1
h(x)=f(g(x))=f(1x)
Step 2
Replace each occurrence of x in f(x) with g(x)=1x
h(x)=[3x]x=g(x)=1x=31x=3x
The dummy variable is not relevant so you can do this in terms of x or y or θ
Step 3
function in simplest form no step 3 needed
For: (gf)(x)
Step 1
r(x)=g(f(x))=g(3x)=
Step 2
Replace each occurrence of x in g(x) with f(x)=3x
r(x)=[1x]x=f(x)=3x=13x
Step 3
function in simplest form no step 3 needed

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