Answer:
You know inverse is shifting the positions of x and y
so consider the first function
f(x)= [tex](x-1)^{5}[/tex] +2
so y = [tex](x-1)^{5}[/tex]+2
no shift x and y positions
x = [tex](y-1)^{5}[/tex] +2
Now solve for y which gives
x - 2 = [tex](y-1)^{5}[/tex]
[tex]\sqrt[5]{x-2}[/tex] = y - 1
y = [tex]\sqrt[5]{x-2}[/tex] + 1
Hence it is inverse to do the same for the other function
2) y = [tex]\sqrt[3]{x}[/tex] -1
shift positions
x = [tex]\sqrt[3]{y}[/tex] -1
x+1 = [tex]\sqrt[3]{y}[/tex]
y = [tex](x+1)^{3}[/tex]
HEnce it is also inverse
