For odd function f(-x)= -f(x)
1) f(-x)= sin(-x) = -sin(x)=-f(x) sin is odd function
2) f(-x) = sin(-2x) = -sin 2x=-f(x)
3) f(-x)= (-x)³+1 = -x³ +1 (not an odd function)To be an odd function, it should be like this:if a function is (x³+1), to be odd f(-x) should be -(x³+1)=-x³-14) f(x)= x/(x²+1)
f(-x) = (-x)/((-x)²+1)= -x/(x²+1)=-f(x)
So, f(-x) gives

,
that means that f(x)= x/(x²+1) is an odd function.
5)f(x) = ∛(2x)
f(-x) = ∛(2*(-x)=∛(2x*(-1)) = ∛(2x)*∛(-1)=
- ∛(2x)= -f(x)
Sample Response: Rotations are rigid transformations, which means they preserve the size, length, shape, and angle measures of the figure. However, the orientation is not preserved. Line segments connecting the center of rotation to a point on the pre-image and the corresponding point on the image have equal length. The line segments connecting corresponding vertices are not parallel.
Answer:
0.07776, 0.3456,0.08704
Step-by-step explanation:
Given that a new surgical procedure is said to be successful 60% of the time
Let X be the no of successes
Then X has only two outcomes and each trial is independent of the other
Hence X is binomial with p = prob of success in a single trial = 0.60
n = Number of operations performed = 5
Prob that
a) all five operations are successful =

(b) exactly three are successful
=
(c) less than two are successful

Collapse the logarithms into one:

Then write both sides as powers of 3:


Simplify the left side and solve for
:



But we're not done yet. Notice that both
and
are negative when
. We can't take the logarithm of a negative number (the result isn't real-valued, anyway), so we throw this solution out, and we're left with just

Answer: 7
Step-by-step explanation:

Divide :)