. Let m and n be the functions given by the following table: 5 20 25...

 

Transcribed Image Text:

. Let m and n be the functions given by the following table: 5 20 25 X m(x) n(x) -2 3 -1 0 Let w = g(t) be the height of water (in feet) that remains at time / (in minutes) in a tank that is draining in such a way that the height of the water is decreasing at a constant rate. The graph of g is given below. Let p(x)=2(x-5) and g(x)=6+0.3x. 10 15 20 3 4 5 15 10 15 6 7 20 15 10 9 10 11 25 20 5 T 13 14 LT5-Use the functions above appropriately to respond to the following questions. Make sure to show how you got your answers or give some kind of justification for your answers, including proper notation. a) Does w= = g(t) have an inverse? If so, explain why and determine the inverse value g(1). If not, explain why not. b) Does the function m(x) have an inverse? If so, explain why and determine the inverse value m(15). If not, explain why not. c) The function p(x) is linear, so it has an inverse. Find a formula for this inverse. d) Note that the function q(x) also has an inverse. Without doing any computations, what is the value of q(q(10)) and why? . Let m and n be the functions given by the following table: 5 20 25 X m(x) n(x) -2 3 -1 0 Let w = g(t) be the height of water (in feet) that remains at time / (in minutes) in a tank that is draining in such a way that the height of the water is decreasing at a constant rate. The graph of g is given below. Let p(x)=2(x-5) and g(x)=6+0.3x. 10 15 20 3 4 5 15 10 15 6 7 20 15 10 9 10 11 25 20 5 T 13 14 LT5-Use the functions above appropriately to respond to the following questions. Make sure to show how you got your answers or give some kind of justification for your answers, including proper notation. a) Does w= = g(t) have an inverse? If so, explain why and determine the inverse value g(1). If not, explain why not. b) Does the function m(x) have an inverse? If so, explain why and determine the inverse value m(15). If not, explain why not. c) The function p(x) is linear, so it has an inverse. Find a formula for this inverse. d) Note that the function q(x) also has an inverse. Without doing any computations, what is the value of q(q(10)) and why?