SOLUTION: The functions are f(x)=2x^2+5x+7 and g(x)=x^3 + 2 The directions say evaluate the following: and identify the domain of each (f+g)(x) I got x^3+2x^2+5x+9 but I dont know what t

Algebra ->  Functions -> SOLUTION: The functions are f(x)=2x^2+5x+7 and g(x)=x^3 + 2 The directions say evaluate the following: and identify the domain of each (f+g)(x) I got x^3+2x^2+5x+9 but I dont know what t      Log On


   

Question 162729: The functions are f(x)=2x^2+5x+7 and g(x)=x^3 + 2
The directions say evaluate the following: and identify the domain of each
(f+g)(x)
I got x^3+2x^2+5x+9 but I dont know what the domain is.
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
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The functions are f(x)=2x^2+5x+7 and g(x)=x^3 + 2
The directions say evaluate the following: and identify the domain of each
(f+g)(x)
I got x^3+2x^2+5x+9 but I dont know what the domain is.
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my answer:
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f+g(x) = f(x) + g(x)
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you got it right again.
domain is all x since nothing to make the answer imaginary or cause a division by 0.
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in general, if the domain is not specified, then the domain is whatever makes the range valid.
there will be 4 graphs.
scan down after each one to get the next plus any additional comments.
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graph of f+g(x) is graph of x^3+2x^2+5x+9 shown below
graph%28800%2C800%2C-9%2C9%2C-1000%2C1000%2Cx%5E3%2B2%2Ax%5E2%2B5%2Ax%2B9%29
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graph of g-f(x) is graph of x^3-2x^2-5x-5 shown below
graph%28800%2C800%2C-9%2C9%2C-600%2C600%2Cx%5E3-2%2Ax%5E2-5%2Ax-5%29
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graph of f*g(x) is graph of x^5 + 5x^4 + 7x^3 + 4x^2 + 10x + 14 shown below

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graph of f/g(x) is graph of (2x^2+5x+7)/(x^3+2) shown below
graph%28800%2C800%2C-9%2C9%2C-10%2C10%2C%282%2Ax%5E2%2B5%2Ax%2B7%29%2F%28x%5E3%2B2%29%29
it appears that the graph is good for all values of x except at x+=+%28-2%29%5E%281%2F3%29 where the value is undefined.
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as x^3 approaches -2 from the right (x^3 is greater than -2), the graph goes positive in a big way.
for example:
if you make x^3 = (-1.9999999999999), which is greater than -2, you'll see that the value of y becomes 3.86114E+13 which is a very large positive number.
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as x^3 approaches -2 from the left (x^3 is smaller than -2), the graph goes negative in a big way.
for example:
if you make x^3 = (-2.0000000000001). which is less than -2, you'll see that the value of y becomes -3.89561E+13 which is a very large negative number.
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the graph does not appear to be able to show this as the intervals between x values appear to be too small to be captured.