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.
Based on the given information, each shelf can hold 9 books. (27/3 = 9) That means 2 additional shelves will hold 18 books. Add 18 to 36 to find the total, which is 54.
Hope that helped you.
=
Multiply both sides by 12, so that we get rid of the fraction in x.
12 · (x+3)/12 = 2/7 · 12
Simplify.
x + 3 = 24/7
Then, subtract 3 from both sides, so that "x" gets isolated.
x = 24/7 - 3
Turn "3" into an improper fraction so that we could find the value of x easier.
3 = 21/3
So :
x = 24/7 - 21/7
Simplify.
x = 3/7
~Hope this helps!~
Answer: The average rate of change is 1 over 3, or just 1/3. The y-values change 1 unit every time the x-values change 3 units, on this interval! hope this helps
First one is c
second one is b
and third one is c
