We Know that For a function to have an inverse function, it must be one-to-one—that
is, it must pass the Horizontal Line Test.
1. On the interval [–pi/2, pi/2], the function
y = sin x is
increasing 2. On the interval [–pi/2, pi/2], y = sin x takes on its full
range of values, [–1, 1] 3. On the interval [–pi/2, pi/2], y = sin x is
one-to-one sin x has an inverse function
on this interval [–pi/2, pi/2]
On the restricted domain [–pi/2, pi/2] y = sin x has a
unique inverse function called the inverse sine function. <span>f(x) = sin−1(x) </span>the range of y=sin x in the domain [–pi/2, pi/2] is [-1,1] the range of y=sin-1 x in the domain [-1,1] is [–pi/2, pi/2]
1. On the interval [0, pi], the function y = cos x is decreasing 2. On the interval [0, pi], y = cos x takes on its full range of values, [–1, 1] 3. On the interval [0, pi], y = cos x is one-to-one cos x has an inverse function on this interval [0, pi]
On the restricted domain [0, pi] y = cos x has a unique inverse function called the inverse sine function. f(x) = cos−1(x) the range of y=cos x in the domain [0, pi] is [-1,1] the range of y=cos-1 x in the domain [-1,1] is [0, pi]
the answer is
<span>the values of the range are different because the domain in which the inverse function exists are different</span>
A 95% confidence interval for a population mean is computed from a sample of size 400. Another 95% confidence interval will be computed from a sample of size 100 drawn from the same population. Choose the best answer to fill in the blank: The interval from the sample of size 400 will be approximately _______as the interval from the sample of size 100.
The order does not matter, so we will be using combinations here. 52C1 is the first one since there is only one possibility. 16C1 is the second. You have to multiply these two, so 52 X 16 = 832.
