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

Question

Mathematics

Gallagher

31 January, 06:16

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

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Mitchell Trevino · 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].