Composition of Two Functions

[nycmath]

See attachment.

[Eigenvalue]

A. Let a(x)=[tex]\sqrt[3]{x}[/tex] and b(x)=3x+4
(a o b)(x)= a(b(x))=[tex]\sqrt[3]{3x+4}[/tex]

B. Let a(x)=|x| and b(x)=2x-3
(a o b)(x)=(a(b(x))=|2x-3|

C. (F o G)(x)
=F(G(x))

|2x-3| when x[tex]\ge[/tex]1.5
=[tex]\sqrt[3]{3(2x-3)+4}[/tex]
=[tex]\sqrt[3]{6x-5}[/tex]

|2x-3| when x<1.5
=[tex]\sqrt[3]{3(-2x+3)+4}[/tex]
=[tex]\sqrt[3]{-6x+13}[/tex]

D. (G o F)(x)
=G(F(x))
=|2[tex]\sqrt[3]{(3x+4)}[/tex]-3|

[nycmath]

A. Let a(x)=[tex]\sqrt[3]{x}[/tex] and b(x)=3x+4
(a o b)(x)= a(b(x))=[tex]\sqrt[3]{3x+4}[/tex]

B. Let a(x)=|x| and b(x)=2x-3
(a o b)(x)=(a(b(x))=|2x-3|

C. (F o G)(x)
=F(G(x))

|2x-3| when x[tex]\ge[/tex]1.5
=[tex]\sqrt[3]{3(2x-3)+4}[/tex]
=[tex]\sqrt[3]{6x-5}[/tex]

|2x-3| when x<1.5
=[tex]\sqrt[3]{3(-2x+3)+4}[/tex]
=[tex]\sqrt[3]{-6x+13}[/tex]

D. (G o F)(x)
=G(F(x))
=|2[tex]\sqrt[3]{(3x+4)}[/tex]-3|

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