find the domain and the range of function of hx sqrtx 6 whe

find the domain and the range of function of
h(x) = sqrt(x) +6   (where x is being square rooted and 6 is not)

Solution

The Domain of a function are the \"allowed\" values that can be inserted into the function and obtain real numbers for answers, i.e. if the number 5 is in the domain, it means that you can put 5 into the function as a value for x. Basically, there are only 2 kinds of values you cannot put into a function. First, you cannot choose values for x that produce a zero in the denominator of a fraction, so for 1/x, the number 0 is not in the function\'s domain. The second is that you cannot choose values for x that result in any negative numbers being square rooted. This is the situation you have here. If x were equal to -1, then you would have to take the square root of negative 1, which is imaginary, not real. Any negative number is prohibited, so the smallest value for x is 0. (FYI, if the 6 were inside the square root, then x could be as small as -6 before you would encounter values resulting in taking the square root of a negative number. Texts and teachers often have preferred styles for reporting domains, but usually, they are represented using something like \"All x, x >= 0\"

The Range of a function are the outputs of the function, i.e. the values h(x) takes on as the values for its domain are inserted. So what values of h(x) will you observe if you were to insert 0, .5, 1, 2, 3, .... to infinity? The smallest number is not zero! Can you get negative values for h(x)? Again the range is expressed but now you use the label of the function, i.e. h(x) >= ___.