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Yes choice B) 1/5 is correct. You are using the correct formula and steps. Nice work.
Here's another way to look at it:
When you visually plot the inverse, you reflect everything over the line y = x. What happens is that every (x,y) point swaps coordinates. So if (1,2) is on g(x), then (2,1) is on the inverse, and vice versa. Swapping the x and y values will swap the nature of the tangent slope.
For any tangent on g(x), its slope is m = (dy)/(dx)
The corresponding slope on the inverse will be n = (dx)/(dy). All that's happened here is that the numerator and denominator flipped. Again because x and y have swapped places. If you wanted, you can picture the xy axis where the vertical axis is the x axis and the horizontal axis is the y axis. That's effectively what is going on here.
So before you found that g'(1) = 5 meaning that m = 5/1 on g(x) at the point (1,2)
So n = 1/m = 1/5 for the point (2,1) on the inverse g function.
Answer:
Length = 13
Step-by-step explanation:
P = 2L + 2W
L = 4W + 1
P = 32
32 = 2(4W +1) + 2W
32 = 8W + 2 + 2W
30 = 10W
W = 3
L = 4(3) + 1
L = 12 + 1
L = 13