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.