Question

What is the inverse of f(x)=2/x

Answer 1

The inverse of the function f(x) = 2/x is the function itself, f-1(x) = 2/x, showing that this function is its own inverse.

Step-by-step explanation:

You asked about the inverse of the function f(x) = 2/x. To find the inverse function, we want to find a function that 'undoes' what f(x) does. An inverse function will take the output of f(x) and get us back to the original input x.

Here are the steps to achieve this:

1. First, replace f(x) with y: y = 2/x.
2. Next, swap the x and y: x = 2/y.
3. Solve this equation for y. When you do this, you get y = 2/x, which means our original function is its own inverse - it is symmetric with respect to the line y = x.
4. You could also write this as f-1(x) = 2/x, where f-1(x) represents the inverse function of f(x).

This also demonstrates an important concept: the reciprocal relationship between a function and its inverse, especially when discussing exponential and logarithmic functions, which are natural inverses of each other.