Final ? - Let f(x) = x2-x-6/x
g(x) = x-3, find
(f+g)(x)
(f-g)(x)
(f/g)(x)
Thanks again
To find (f+g)(x), you need to add the functions f(x) and g(x) together.
First, let's find f(x) + g(x):
f(x) = x^2 - x - 6 / x
g(x) = x - 3
To add them together, simply replace f(x) and g(x) with their respective expressions:
(f+g)(x) = (x^2 - x - 6 / x) + (x - 3)
Now, simplify the expression by finding a common denominator and combining like terms:
(f+g)(x) = (x^2 - x - 6 + x(x - 3)) / x
(f+g)(x) = (x^2 - x - 6 + x^2 - 3x) / x
(f+g)(x) = (2x^2 - 4x - 6) / x
So, (f+g)(x) = 2x - 4.
Next, to find (f-g)(x), you need to subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x)
(f-g)(x) = (x^2 - x - 6 / x) - (x - 3)
Using the same process as above, simplify the expression:
(f-g)(x) = (x^2 - x - 6 - x(x - 3)) / x
(f-g)(x) = (x^2 - x - 6 - x^2 + 3x) / x
(f-g)(x) = (-2x + 6) / x
So, (f-g)(x) = -2 + 6/x.
Finally, to find (f/g)(x), you need to divide f(x) by g(x):
(f/g)(x) = f(x) / g(x)
(f/g)(x) = (x^2 - x - 6 / x) / (x - 3)
To divide fractions, multiply the first fraction by the reciprocal of the second fraction:
(f/g)(x) = (x^2 - x - 6 / x) * (1 / (x - 3))
(f/g)(x) = (x^2 - x - 6) / (x * (x - 3))
(f/g)(x) = (x^2 - x - 6) / (x^2 - 3x)
Therefore, (f/g)(x) = (x^2 - x - 6) / (x^2 - 3x).