For the functions f left parenthesis x right parenthesis equals 6 minus x squared and g left parenthesis x right parenthesis equals x squared plus 4 x minus 12, find fplusg, fminusg, fg, and StartFraction f Over g EndFraction . Determine the domain for each function.

Step-by-step explanation:

Given the functions

F(x) = 6-x²

G(x) = x²+4x-12

A) we are to find F(x)+g(x)

F(x)+G(x) = 6-x²+x²+4x-12

F(x)+G(x) = 6+0+4x-12

F(x)+G(x) = 4x+6-12

F(x)+G(x) = 4x-6

The domain of the function is the values of x for which the expression exists. The expression exists on all real interval i.e xER

F(x)-g(x) = 6-x²-(x²+4x-12)

F(x)-g(x) = 6-x²-x²-4x+12

F(x)-g(x) = 6-2x²+4x+12

F(x)-g(x) = -2x²+4x+6

The domain of the function is the values of x for which the expression exists. The expression exists on all real interval i.e xER

3) F(x)/G(x)

= 6-x²/x²+4x-12

The domain of the function is the values of x for which the expression exists. The expression exists on all real interval i.e xER