SOLUTION: Let f(x) = (x^2 + 3x - 4) and g(x) = (x + 4)
a. find f*g and state the domain
b. find f/g and state the domain
Algebra.Com
Question 1020071: Let f(x) = (x^2 + 3x - 4) and g(x) = (x + 4)
a. find f*g and state the domain
b. find f/g and state the domain
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ \cdot\ g(x)\ =\ (x^2\ +\ 3x\ -\ 4)(x\ +\ 4))
If it pleases you to do so, you can multiply this out to get a 3rd degree polynomial. But since it is a polynomial, the domain is all real numbers.
}{g(x)}\ =\ \frac{x^2\ +\ 3x\ -\ 4}{x\ +\ 4}\ =\ \frac{(x\ +\ 4)(x\ -\ 1)}{x\ +\ 4}\ =\ \ x\ -\ 1)
Before simplification, this was a rational function so the domain is all real numbers excluding any value that would make the denominator equal zero.
Hence \ \text{ U }\ (-4,\infty)\ =\ \{x\ \in\ \mathbb{R}\ :\ x\ \not =\ 4\})
John
My calculator said it, I believe it, that settles it
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