8/22 Composition of Functions

[Eigenvalue]

Here are some questions that pertain to composition of functions:

[Eigenvalue]

1. f(g(x))=3(2[tex]\sqrt{x-3)}[/tex])+7

f(g(x))=6[tex]\sqrt{x-3}[/tex]+7

When x=3:

f(g(3))=6[tex]\sqrt{3-3}[/tex]+7=7

g(f(x))=2[tex]\sqrt{3x+7-3}[/tex]

g(f(x))=2[tex]\sqrt{3x+4}[/tex]

When x=3:

g(f(3))=2[tex]\sqrt{9+4}[/tex]=2[tex]\sqrt{13}[/tex]

Note: f(g(x)).does not have to equal g(f(x))

[nycmath]

1. f(g(x))=3(2[tex]\sqrt{x-3)}[/tex])+7

f(g(x))=6[tex]\sqrt{x-3}[/tex]+7

When x=3:

f(g(3))=6[tex]\sqrt{3-3}[/tex]+7=7

g(f(x))=2[tex]\sqrt{3x+7-3}[/tex]

g(f(x))=2[tex]\sqrt{3x+4}[/tex]

When x=3:

g(f(3))=2[tex]\sqrt{9+4}[/tex]=2[tex]\sqrt{13}[/tex]

Note: f(g(x)).does not have to equal g(f(x))

Great step by step work.