What is the inverse of the function f(x)=√(3x-1) ?

Answer 1

We use the standard method of finding inverses. Note that, so that we have a unique inverse, we should assume that y is greater than or equal to 0. In order for 3x - 1 >= 0, x >= 1/3

Then, y = sqrt(3x - 1);

squaring both sides, y^2 = 3x - 1

3x = y^2 + 1

x = (y^2 + 1)/3

we then switch x and y in order to define this as an inverse.

f^-1(x) = (x^2 + 1)/3 x >= 0