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Question

Part 1
Let ​f(x)equals6minusx and ​g(x)equalsStartFraction 1 Over x EndFraction
. Perform the function operation and then find the domain of the result.
StartFraction f Over g EndFraction
​(x)

Answer 1

To find the result of the function operation, we first need to divide f(x) by g(x):

StartFraction f Over g EndFraction (x) = f(x) / g(x)
= (6 - x) / (1/x)
= (6 - x) * x
= 6x - x^2

Now, to find the domain of this function, we need to consider the values of x for which the function is defined. Since the original function g(x) = 1/x is not defined at x = 0 (division by zero is not allowed), we need to exclude x = 0 from the domain of the new function 6x - x^2.

Therefore, the domain of StartFraction f Over g EndFraction (x) = 6x - x^2 is all real numbers except for x = 0.