What is the value of f^{-1)(6)

 4

Start at 6 on the y axis. Draw an arrow so that it horizontally moves to the blue curve. Then draw an arrow straight down to vertically drop to x = 4

See the diagram below.

Follow this process in reverse to see that x = 4 leads straight up to the blue curve, and then to the left to land on y = 6. Keep in mind that the inverse reverses the input and output process, which is why I started with y instead of x.

The number of buttons in tin C is 17.
x+4x+x-7= 137
combine like terms
6x-7=137
isolate the variable by adding 7 to both sides
6x=144
divide
x=24
but remember, tin c is x-7 so plug the 24 in, and the answer is 17.