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
Answer:
(base × height) × 0.5
Step-by-step explanation:
Formula of the Area of a Triangle => (base × height) × 0.5
Answer:
0,-1
Step-by-step explanation:
Answer:
Step-by-step explanation:
angle 1 and angle 2 add to 180 degree because they are supplementary angel and in supplementary angle sum of two angles is 180 degree
angle 1 and angle 3 is equal as they are vetically opposite angles and vertically opposite angles are always equal.
angle 3 and 4 add to 180 degree because they are supplementary angle and in supplementary angle sum of two angles id 180 degree.
angle 2 and angle 4 are equal because they are vertically opposite angles and vertically opposite angles are always equal.
Answer:
4 mechanical pencils
Step-by-step explanation:
Each notebook is worth $2.99
So buying 3 of the notebooks would leave her with $8.97
Then, $15.00 - $8.97= $6.05
