What is the inverse of f if f(x)= ^3/x-5
Where / means square root
To find the inverse of a function, we start by replacing f(x) with y and then solve for x.
Given f(x) = √(3/x - 5)
y = √(3/x - 5)
Now, we switch x and y and solve for y:
x = √(3/y - 5)
Square both sides to eliminate the square root:
x^2 = 3/y - 5
Now, isolate y:
x^2 = 3/y - 5
x^2 + 5 = 3/y
y = 3/(x^2 + 5)
Therefore, the inverse of f(x) = √(3/x - 5) is f^(-1)(x) = 3/(x^2 + 5).