SOLUTION: i dont know where to start or anything f(x)=x+2 divided by the square root of (2x-7) g(x)=x-3 domain of f*g

Question 260056: i dont know where to start or anything
f(x)=x+2 divided by the square root of (2x-7) g(x)=x-3
domain of f*g
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
i dont know where to start or anything
f(x)=x+2 divided by the square root of (2x-7)and g(x)=x-3
Find the domain of f*g.
Remember that (f*g)(x) = f(x)*g(x) so
(f*g)(x) = [(x+2)/sqrt(2x-7)]*(x-3) =
[(x+2)*(x-3)/sqrt(2x-7) =
[x^2 - x - 6]/sqrt(2x-7)
The domain of this function is the set of values for x that are allowed for this expression to be defined.
The expression is defined except when the denominator is 0. The denominator becomes 0 when sqrt(2x-7) = 0.
sqrt(2x-7) = 0 if 2x-7 = 0 which is when x = 7/2.
The domain then is all real numbers except 7/2.
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