SOLUTION: Perform the operation and state the domain and range of g(f(x)) f(x)= x^2+3x; g(x)= 2x+1

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Question 892421: Perform the operation and state the domain and range of g(f(x))
f(x)= x^2+3x; g(x)= 2x+1
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
g%28f%29=2f%2B1
g%28f%29=2%28x%5E2%2B3x%29%2B1
g%28f%29=2x%5E2%2B6x%2B1
Complete the square to convert to vertex form,
g%28f%29=2%28x%5E2%2B3x%29%2B1
g%28f%29=2%28x%5E2%2B3x%2B9%2F4%29%2B1-2%289%2F4%29
g%28f%29=2%28x%2B3%2F2%29%5E2%2B2%2F2-9%2F2
g%28f%29=2%28x%2B3%2F2%29%5E2-7%2F2
There are no constraints on the domain : (-infinity,infinity).
The function has a minimum value of -7%2F2 so the range is
[-7%2F2,infinity)
.
.
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graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2x%5E2%2B6x%2B1%29