find the inverse of f(x)=1/x^5

Question

i do not know how to do this. can someone please show me the steps to solving this problem.

Answer 1

Start by writing y = 1/x⁵. Now swap x and y and then solve for y.

x = 1/y⁵

xy⁵ = 1

y⁵ = 1/x

y = 1/x^1/5

Thus you have f^-1(x) = 1/x^1/5

Answer 2

y = 1/x^5

To find the inverse function, you need to switch x and y, and solve for y,

x = 1/y^5

y = 1/x^(1/5)

Answer: f^-1(x) =1/x^(1/5)

Answer 3

Solve the function for "x" and switch places for "x" and "y" 
√a = a ^1/2
~~~~~~~~
                 1
f(x) = y = ——   (xy ≠ 0) 
                 x⁵   

yx⁵ = 1 ---> x⁵ = 1 / y ---> x = (1/y)^1/5  

y = (1/x)^1/5

And the final answer is:
                      1               
f ^-1 (x)   =   ——    (xy ≠ 0) 
                    x^1/5 

Answer 4

Let   y=1/x^5      

then x^5=1/y

       x=(1/y)^1/5   -----> x=1/y^1/5 ------- I

as  f(x)=y       ------>     x=f ^-1y       --------II

from equation I & II,     f ^-1 y=1/y^1/5     ,    now replacing y by x

                               f^-1( x )=1/x^1/5