Since f(x) is (strictly) increasing, we know that it is one-to-one and has an inverse f^(-1)(x). Then we can apply the inverse function theorem. Suppose f(a) = b and a = f^(-1)(b). By definition of inverse function, we have
f^(-1)(f(x)) = x
Differentiating with the chain rule gives
(f^(-1))'(f(x)) f'(x) = 1
so that
(f^(-1))'(f(x)) = 1/f'(x)
Let x = a; then
(f^(-1))'(f(a)) = 1/f'(a)
(f^(-1))'(b) = 1/f'(a)
In particular, we take a = 2 and b = 7; then
(f^(-1))'(7) = 1/f'(2) = 1/5
Let p = weight of papaya and g = weight of grapes.
Then (3/4)g = (3/5)p. Since the weight of grapes is x + 28,
(3/4)(x + 28) = (3/5)p. We must solve for x. To do this, mult. both sides by (5/3):
(5/3)(3/4)(x+28) = (5/3)(3/5)p
Then p = (15/9)(x+28), or (after reduction), p = (5/3)(x+28).
Answer:
C, or 18.0
Step-by-step explanation:
The SAS theorem provides that the area is 17.97, which rounds up to 18.0, giving you C as the answer. The other two are far too high for the given values.
Answer:
2pi/5
Step-by-step explanation:
The only thing in this equation that affect the period is the '5' in front of the 'x'
cos period is usually 2pi
this is compressed by 5
period = 2pi/ 5
Answer:
Range is number of copies produced and set of values is; 1 ≤ N ≤ 200
Domain; Cost of publishing book in dollars; set of values are; $710 ≤ N ≤ $2700
Step-by-step explanation:
Range is a set of all the possible output values in a function while domain is the set of all possible input values.
Now, the function is given as;
C = 10N + 700
Where;
C is the cost of publishing the book in dollars
N is the number of copies of books produced
Thus, the domain will be a set of N values while Range will be a set of C values.
We are told that the first printing can produce up to 200 copies of the book.
That means a maximum of 200 books and a minimum of 1.
Thus;
Range is; 1 ≤ N ≤ 200
Maximum possible cost of the 200 books is;
C = 10(200) + 700
C = $2700
Minimum cost which will be for 1 book will be;
C = 10(1) + 700
C = $710
Thus,domain is;
$710 ≤ N ≤ $2700
