FUNCTIONS - 4

If f(x)=20^x, find f^-1(¹/₄₀₀)

Solution

f(x)=20^x

let f(x) = y

then y=20^x

we change it into logarithmic form, and it will be,

log₂₀y=x;

x= log₂₀y after re-arranging,

Then we interchange x and y variables,

y^-1 = log₂₀x

f^-1(x) = log₂₀x

f^-1(¹/₄₀₀) = log₂₀(¹/₄₀₀)

              =  log₂₀(400^-1)

  

              = -1 x log₂₀(400); 400 is a perfect square giving (20 x 20=20²)

              = -1 x log₂₀(20)²

   

              = -1 x 2 x log₂₀20

  

              = -1 x 2 x 1

              = -2

Hence f^-1(¹/400) = -2