Graph the function and its inverse:  f(x)= sqrt x-3

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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.

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