Find Functions f and g

[nycmath]

See attachment.

[Math Tutor]

A. [tex]H(x)=(1+x^2)^3[/tex]

Take the inner expression as g and the outer power as f:

[tex]g(x)=1+x^2[/tex] and [tex]f(x)=x^3[/tex]

Then [tex]f(g(x))=(1+x^2)^3=H(x)[/tex]

[Eigenvalue]

Questions A and B:

[Eigenvalue]

Question C:

[nycmath]

A. [tex]H(x)=(1+x^2)^3[/tex]

Take the inner expression as g and the outer power as f:

[tex]g(x)=1+x^2[/tex] and [tex]f(x)=x^3[/tex]

Then [tex]f(g(x))=(1+x^2)^3=H(x)[/tex]

Nice. Thanks.

[nycmath]

Questions A and B:

Yes and thanks.