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Recall the inverse function theorem: if f(x) has an inverse, and if f(a) = b and a = f⁻¹(b), then
f⁻¹(f(x)) = x ⇒ (f⁻¹)'(f(x)) • f'(x) = 1 ⇒ (f⁻¹)'(f(x)) = 1/f'(x)
⇒ (f⁻¹)'(b) = 1/f'(a)
Let b = 10. Then pick the function f(x) such that f(a) = 10 and f'(a) = -8 for some number a.
Answer:
Diagram attached
AJ = 8.75 in.
Step-by-step explanation:
Since triangles HBA & HKJ are similar,
BH/AH = KH/JH
3 in /5.25 in = 8 in /JH
JH = 14 in
JA = JH - AH = JH - 5.25 in = 8.75 in
HJ = 14 in.
AJ = 14 in - 5.25 in
AJ = 8.75 in.
Answer:
Step-by-step explanation:
If 75 percent is 180 pages, we need to find the amount of pages the remaining 25 percent of the book has and add that to 180 pages because 75+25 = 100. 75/3 is equal to 25.
75:180 =
25:60.
By dividing the ratio, we found out that if Logan read 25 percent of his book, he would have read 60 pages.
180 + 60 = 240.
The total number of pages is 240
Gradient =
Change in Y
———————
Change in X
Change in Y is 18 - 14 = 4
Change in X is -20 - 30 = -50
Therefore the gradient is 4/-50 which is then simplified to - (2/25)
