Question 528003: Need help once again, can't seem to figure this out.
Let h and g be two functions defined by
h(x)=(5+x)(-6+x)
g(x)=2-x
for any real number x.
Find h/g(3) and then find all values that are NOT in the domain of h/g. If there is more than one value, separate them with commas.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! h(x)=(5+x)(-6+x)
h(3)=(5+3)(-6+3)
h(3)=(8)(-3)
h(3) = -24
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g(x)=2-x
g(3)=2-3
g(3) = -1
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(h/g)(x) = (h(x))/(g(x))
(h/g)(3) = (h(3))/(g(3))
(h/g)(3) = -24/(-1)
(h/g)(3) = 24
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Since you CANNOT divide by zero, this means that the denominator g(x) cannot be zero.
If it were, then g(x) = 0 would mean that 2-x = 0 and that x = 2
So x = 2 makes the denominator zero. So we must exclude that from the domain.
If you need more help, email me at jim_thompson5910@hotmail.com
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Jim
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