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Question 64614: Given f(x)=1/x and g(x)=(x+1)/(x-2), find f/g(x) and state its domain.
Answer by praseenakos@yahoo.com(507)   (Show Source):
You can put this solution on YOUR website! QUESTION:
Given f(x)=1/x and g(x)=(x+1)/(x-2), find f(x)/ g(x) and state its domain.
ANSWER:
f(x)/ g(x) = (1/x )/ ((x+1)/(x-2))
While dividing two rational expressions, take the reciprocal of the divisor(that is f(x)) and multiply it with the divident ( that is g(x) )
==> f(x)/ g(x) = (1/x )* [(x-2)/(x+1)]
==> = [ 1 * (x-2)]/[x * (x+1)]
==> = (x-2)/( x*x - x*1)
==> f(x)/ g(x) = ( x-2)/(x^2 -x )
OR we can write, f(x)/ g(x) = (x-2)/x(x + 1)
In the denominator, we have x(x + 1)
The values, x = 0 and x = -1 make the denominator zero.
That means for values, x = 0, -1 the function is not defined.
So we can say that domain of f(x)/ g(x) is set of all real numbers except 0 and -1
That is Domain = R - {0, -1}
Hope you understood.
Regards.
Praseena.
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