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:
18
Step-by-step explanation:
I did the problem
24 times 16 is 384 and 384 times 18 is 6912
Answer:
8 bunches
Step-by-step explanation:
4/8 9/18
Answer:
the answer will be 28
Step-by-step explanation:
180-47-31=102
since vertical angles have the same value the top angles for both triangles will be 102 degrees
102+50=152
180-152=x
28=x
Answer:
Area of ΔQRS = 2.3 square inches
Step-by-step explanation:
From the given information,
<S + <Q + <R = 
51 + 44 + <R =
95 + <R =
<R = - 95
= 
<R =
Applying the Sine rule, we have;
= 
= 
Using =
= 
r = 
= 2.9483
r = 2.9 inches
Also, =
=
q = 
= 2.0559
q = 2.0 inches
From Herons formula,
Area of a triangle = 
s = 
= 3.6
Area of ΔQRS = 
= 2.2895
Area of ΔQRS = 2.3 square inches
