Answer
f(f^-(x))=x
f^-(f(x))=x
Work Step by Step
Step 1: y=(2x^3+1)^1/5
y^5=2x^3+1, y^5-1=2x^3, y^5-1/2=x^3, x=\sqrt[3] (y^5 -1)/2
step 2: \sqrt[3] (x^5 -1)/2=f^-1(x)
The domain of f ^-1:(-\infty,\infty), Range of f^-1(-\infty,\infty) ;
f(f^-1(x))=(2(\sqrt[3]( x^5 -1)/2)^3+1)^1/5=(2((x^5-1)/2)+1)^1/5=((x^5 -1)+1)^1/5=(x^5)^1/5=x
f^-1(f(X))=\sqrt[3] ([(2x^3 +1)^1/5]^5 -1)/2=\sqrt[3] ((2X^3+1)-1)/2=\sqrt[3] 2x^3/2=x
