How do you describe the interval(s) on which the function is continuous, using interval notation?

f(x) = x sqrt (x + 6)

1 Answer
Jan 22, 2018

The function is a composition and multiplication of continuous functions, so as long as it is defined, #f# is continuous.

Explanation:

The function #f# is defined for all values #x# such that the expression inside the square root is non-negative, that is when #x+6 >=0#, or equivalently when #x>=-6#. Within that domain, #x+6# is a continuous function, the square root is a continuous function and the multiplication by #x# is also continuous.

Then, #f# is continuous for all #x >=-6#; in interval notation, in the interval #[-6, +oo)#