Suppose that the functions f and g are defined as follows. f(x)=(x+6)(x−2) g(x)=−5x−5 ​ (a) Find ( g f ​ )(6). (b) Find all values that are NOT in the domain of g f ​ . If there is more than one value, separate them with commas. (a) ( g f ​ )(6)= (b) Value(s) that are NOT in the domain of g f ​ : The functions s and t are defined as follows. s(x)=−x+2 t(x)=−2x 2 −2 ​ Find the value of t(s(−1)). Suppose that the functions p and q are defined as follows. p(x)=−x−1 q(x)=x 2 −2 ​ Find the following. (q∘p)(−4)= (p∘q)(−4)= ​ A car rental company's standard charge includes an initial fee plus an additional fee for each mille driven. The standard charge S (in dotlars) is given by the function S=0.50M+14.95, where M is the number of miles driven. The company aiso offers an option to insure the car against damaget The insurance charge I (in dollars) is given by the function I=0.25.M+4.90. Let C be the total charge (in doltars) for a rental that includes insurance. Write an equation relating C to M. 5 implify your answer as ing is possible. Find the difference quotient h f(x+h)−f(x) ​ , where h  =0, for the function below. f(x)=−x 2 +3x−2 Simplify your answer as much as possible. Suppose H(x)=7x 6 −2 Find two functions f and g such that (f∘g)(x)=H(x). Neither function can be the identity function. (There may be more than one correct answer.)