Answer:
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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
No.
If players were proportional to teams, there would be the same number of players on each team.
Answer:
(a) 16 ft/s
(b) 1.5 s
Step-by-step explanation:
(a) Put 1 where t is in the expression and do the arithmetic:
-32×1 +48 = 16 . . . . feet per second
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(b) Use the hint and solve for t:
-32t +48 = 0
t -1.5 = 0 . . . . . divide by 32
t = 1.5 . . . . . . . . add 1.5
The ball reaches its maximum height after 1.5 seconds.
Answer:
✧ We know , Reflection of a point on x - axis remains the x - co-ordinate same but the sign of y - coordinate changes i.e P ( x , y ) ⇢ P' ( x , - y ). So, the image of the point ( 8 , 10 ) under the reflection on x - axis is :
A ( 8 , 10 ) ⇢A' ( 8 , -10 )
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