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

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.