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:
Its A/
Step-by-step explanation:
That would be Option C (Answer).
Answer:
u•u = 17
u•v = 13
v•u = u•v = 17
v•u/u•u = 13/17
Step-by-step explanation:
Given 2 column matrices
u = [-1 4] and v = [7 5]
Note that when computing product, we will multiply component wise.
To compute u times u, we will take the dot product of both column matrix.
u•u = [-1 4] • [-1 4]
u•u = (-1)(-1) + (4)(4)
u•u = 1+16
u•u = 17
To compute u times v, we will take the dot product of column matrix u and column matrix v.
u•v = [-1 4] • [7 5]
u•v = (-1)(7) + (4)(5)
u•v = -7+20
u•v = 13
v•u/u•u can be gotten by simply substituting the resulting values.
v•u/u•u = 13/17
Answer:
Step-by-step explanation:
you see 12=12 (side)
6=6 (side)
116°=116°(angle between sides)
now what can be the answer?
two sides and one angle equal
so SAS