Question

Let f(x) = -20x2 + 14x + 12 and g(x) = 5x - 6. Find F/G and state its domain.

a. –4x – 2; all real numbers except x =6/5
b. 5x - 6; all real numbers
c. –4x – 2; all real numbers
d.5x - 6; all real numbers except x =6/5

Answer 1

f(x)=-20x^2+14x+12
=-20x^2-10x+24x+12
=-10x(2x+1)+12(2x+1)
=(-10x+12)(2x+1)
g(x)=5x-6\[\frac{ f(x) }{ g(x) }=\frac{ (-10x+12)(2x+1) }{ (5x-6) }\]

Answer 2

\[\frac{ f(x) }{ g(x) }=\frac{ -2(5x-6)(2x+1) }{ (5x-6) }\]
\[=-2(2x+1)\]
=-4x-2

Answer 3

to find domain of f(x)/g(x), if (5x-6)=0 then it will give divide by 0 error.
so,\[(5x-6) \neq 0\]
\[x \neq \frac{ 6 }{ 5 }\]

Answer 4

so domain is all real numbers except 6/5
and f(x)/g(x)=-4x-2

Answer 5

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Answer 6

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Answer 7

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