For the function f(x)= sqrt(x-3), determine the domain and the range. Does f(x) have an inverse?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function given is f(x) = sqrt(x - 3)

The domain of a function is all the values that the independent variable can take for real values of the dependent variable.

Here (x - 3) should not be negative

(x - 3) >= 0

=> x >= 3

The domain is [3, inf.)

The range of the function is [0, inf.)

To find the inverse of the function, let y = sqrt(x - 3)

=> y^2 = (x - 3)

=> x = y^2 + 3

interchange x and y

y = x^2 + 3

The inverse function f^-1(x) = x^2 + 3

This is not a valid solution as both x and -x give the same value for f(x). Therefore the function f(x) does not have an inverse.

The domain of f(x) is [3, inf.) and the range is [0, inf.). The function does not have an inverse.

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