Let f(x) = (3x^2 - 10x - 25)/(x + 1) and g(x) = (3x^2 - 10x - 25)/(3x^2 + 11x + 10). Find the sum of all real numbers that are not in the domain of f(g(x)).
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If you could give me the answer to this question quickly, that would be very helpful. Thanks!
+9479 \(f(\,g(x)\,)\,=\,\frac{3(\,g(x)\,)^2-\,10(\,g(x)\,)\,-\,25}{g(x)\,+\,1}\)
f( g(x) ) is undefined when g(x) is undefined, and g(x) is undefined when...
3x2 + 11x + 10 = 0
3x2 + 6x + 5x + 10 = 0
3x(x + 2) + 5(x + 2) = 0
(x + 2)(3x + 5) = 0
x = -2 and x = -5/3
f( g(x) ) is also undefined when
g(x) + 1 = 0
\(\frac{3x^2-10x-25}{3x^2+11x+10}+1\,=\,0 \\~\\ \frac{3x^2-10x-25}{3x^2+11x+10}+\frac{3x^2+11x+10}{3x^2+11x+10}\,=\,0 \\~\\ \frac{6x^2+x-15}{3x^2+11x+10}\,=\,0\)
6x2 + x - 15 = 0
6x2 - 9x + 10x - 15 = 0
3x(2x - 3) + 5(2x - 3) = 0
(2x - 3)(3x + 5) = 0
x = 3/2 and x = -5/3
f(g(x)) is undefined when x = -2 , x = -5/3 , and x = 3/2 .
-2 + -5/3 + 3/2 = -13/6
+9479 \(f(\,g(x)\,)\,=\,\frac{3(\,g(x)\,)^2-\,10(\,g(x)\,)\,-\,25}{g(x)\,+\,1}\)
f( g(x) ) is undefined when g(x) is undefined, and g(x) is undefined when...
3x2 + 11x + 10 = 0
3x2 + 6x + 5x + 10 = 0
3x(x + 2) + 5(x + 2) = 0
(x + 2)(3x + 5) = 0
x = -2 and x = -5/3
f( g(x) ) is also undefined when
g(x) + 1 = 0
\(\frac{3x^2-10x-25}{3x^2+11x+10}+1\,=\,0 \\~\\ \frac{3x^2-10x-25}{3x^2+11x+10}+\frac{3x^2+11x+10}{3x^2+11x+10}\,=\,0 \\~\\ \frac{6x^2+x-15}{3x^2+11x+10}\,=\,0\)
6x2 + x - 15 = 0
6x2 - 9x + 10x - 15 = 0
3x(2x - 3) + 5(2x - 3) = 0
(2x - 3)(3x + 5) = 0
x = 3/2 and x = -5/3
f(g(x)) is undefined when x = -2 , x = -5/3 , and x = 3/2 .
-2 + -5/3 + 3/2 = -13/6
