+0  
 
0
83
2
avatar

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)).

 

--

 

If you could give me the answer to this question quickly, that would be very helpful. Thanks!

Guest Jan 29, 2018

Best Answer 

 #1
avatar+6943 
+3

\(f(\,g(x)\,)\,=\,\frac{3(\,g(x)\,)^2-\,10(\,g(x)\,)\,-\,25}{g(x)\,+\,1}\)

 

 

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

hectictar  Jan 29, 2018
Sort: 

2+0 Answers

 #1
avatar+6943 
+3
Best Answer

\(f(\,g(x)\,)\,=\,\frac{3(\,g(x)\,)^2-\,10(\,g(x)\,)\,-\,25}{g(x)\,+\,1}\)

 

 

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

hectictar  Jan 29, 2018
 #2
avatar+85609 
+1

Very nice, hectictar...!!!

 

cool cool cool

CPhill  Jan 29, 2018

23 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details