Answer:
See the works below.
Step-by-step explanation:
To find the inverse of a function, we need to swap the components until we have the variable at 1 side of the equation.
14. [tex]h(n)=\sqrt[3]{n+2} -2[/tex]
The variable = n, therefore we swap the component until we get n = ...
[tex]h(n)=\sqrt[3]{n+2} -2[/tex]
[tex]\sqrt[3]{n+2} =h(n)+2[/tex]
[tex](\sqrt[3]{n+2} )^3=(h(n)+2)^3[/tex]
[tex]n+2=h(n)^3+3(h(n))^2(2)+3(h(n))(2)^2+2^3[/tex]
[tex]n+2=h(n)^3+6h(n)^2+12h(n)+8[/tex]
[tex]n=h(n)^3+6h(n)^2+12h(n)+8-2[/tex]
[tex]n=h(n)^3+6h(n)^2+12h(n)+6[/tex]
Now, we replace the term [tex]n[/tex] with [tex]h^{-1}(n)[/tex] and term [tex]h(n)[/tex] with [tex]n[/tex], then it will become:
[tex]\bf h^{-1}(n)=n^3+6n^2+12n+6[/tex]
15. [tex]g(x)=-x+2[/tex]
The variable = x, therefore we swap the component until we get x = ...
[tex]g(x)=-x+2[/tex]
[tex]x=-g(x)+2[/tex]
Now, we replace the term [tex]x[/tex] with [tex]g^{-1}(x)[/tex] and term [tex]g(x)[/tex] with [tex]x[/tex], then it will become:
[tex]\bf g^{-1}(x)=-x+2[/tex]
