Question

Let f(x) = -6x + 3 and g(x) = 5x + 4. Find and state its domain. -30x2 - 9x + 12; all real numbers except x = 4 -18x2 - 39x + 20; all real numbers except x = 1 -18x2 - 39x + 20; all real numbers -30x2 - 9x + 12; all real numbers

Answer 1

Unsure of whether this is a composite function or not.  It does look like you've multiplied f(x) and g(x) together.

Looking at -30x2 - 9x + 12, we see immediately that this is a polynomial function.  Because of that, the domain is the set of all real numbers.  The graph of this poly opens down, so the max value is at the vertex, x = -b / (2a).

Here a= -6 and b= -9, so this x-value is -(-9) / (2*(-6)), or  x = 9/12, or x = 3/4.

By subst. 3/4 for x in the poly., we find that the max y value is 4.83.  Thus,the rante is (-infinity, 4.83].