Hello! I am doing homework and need to know, what is the algebra way of doing this? If anyone could provide an explanation and answer it would be appreciated. THANK YOU TUTORS FOR YOUR HELP

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet} of the outer ripple is 1" (t) = 0.6515 where t is the time, in seconds. after the pebble strikes the water. The circumference of the circle is given by the function 0 [1") = 2m\". What would be the circumference of the circular ripple after t seconds? 0 C [1' {} = 211' {Ut} = 1.3111 0 C (rim. = 2171* + 0.65: O C [1' () = 0-135(211-1') = 1.3m o C(r); = 2w{0.65t] = 1.3m Which of the following shows the inverse of the function given below? y 3 Oy= 2-3x O y = -3 Oy= 3x - 2 Oy= - 2Which of the following shows the inverse of the function given below? y = 3x + 9 Oy= :+9 Oy= + 3 Oy= - 3 Oy = 3x - 9Which of the following statements is always true? 0 Given two functions f (it) and g (a), if f [g (3)) = m, then f[:1:) = 3'1 {3:} 0 Given two functions f [3:] and g {1:}, if f [g (3)) = m, then f [$J and g [3) are inverses. @ Given two functions f [11:] and g {a}, if f [g[:a}) = g [f (3)] = a, then f[:1:) = y'1 {3:} and 9(a) = r1 (93]- 0 Given two functions f [93} and g {at}, ifg [5" (En = m, then 5: [3:] = f_1 [in]. The functions f (3:) and g (at) are shown below. fti) = 5329 901:): 84-293: Which of the following correctly veries whether or not f (in) and g (at) are inverse functions? C) Sinceg [f (:10) = m. then f [LBJ and g (as) are inverses. C) Since f[g[:1:)) = g [f (32)] = :11, then f [it] andg [o] are inverses. 0 Since 3' [g (on 75 m. then 3"[13] and g {at} are not inverses. 0 Since 3' [g [on = 9:. then f [m] and g (3:) are inverses. The graphs of f (x) and g (a) are shown. f(x) g(x) -2 12 -2 4 Image Source: Developer created image by V. Kiser using Desmos and Google Drawings. Use the graphs to evaluate the following- . f (1) = . 9 (-5) = . f (9 (1)) = . f (g (-1.5)) = . 9 (f (-4) ) = . f (f (-1) ) =Your car's gas mileage is an average of 25 miles per gallon. Let g represent the m E ! where m is the number of miles you drove. The total cost of lling your car's gas number of gallons of gas you need to put in your car such that g (m) = tank is C(x} where C is cost in dollars and x is the number of gallons purchased. What does the expression C (y (171)) represent