Graph the function and its inverse: f(x)= sqrt x-3
Plug several x values in the equation of the function such that:
`x = 3 =gt f(x) = sqrt(3-3) = 0`
`` `x = 4 =gt f(x) = sqrt(4-3) = sqrt1 = 1`
Notice that values of x are larger or equal to 3, otherwise the value under the radical would be negative and the function would exist no more.
The graph of the function `f(x) = sqrt(x-3)` is a curve that hosts the points (3;0);(4;1).
The graph of the inverse function is the reflection of the graph of the function across the line y = x.
Evaluating the equation of the inverse function yields:
`y= sqrt(x - 3) =gt y^2 = x - 3 =gt x = y^2 + 3`
`f^-1(x) = x^2+3`
The equation of the inverse function is `f^-1(x) = x^2 + 3` and the graph of this function is the reflection of the curve`y = sqrt(x-3)` across the line y=x.