For a function (fn) to be odd:
f(x) = - f(-x)
For a fn to be even:
f(x) = f(-x)
For a fn to be neither even nor odd
f(x) != f(-x) [No Relation]
(-x)^n = x^n for n -> even
(-x)^n = -x^n for n -> odd
In your example:
f(x) = -4x^3 + 4x
f(-x) = -4 (-x)^3 + 4 (-x)^1 ( 3 and 1 are odd powers )
f(-x) = 4x^3 - 4x (take -1 common to do the check)
f(-x) = -( -4x^3 + 4x ) = - f(x) [between the bracket was the original fn]
f(x) = - f(-x)
so the function is odd also called symmetric about the origin
Answer:
12.4
Step-by-step explanation:
Answer:
103,000
Step-by-step explanation:
Use your knowledge of decimal arithmetic. Or, use a calculator.
100,000(1 +.03) = 100,000·1.03 = 1000·103 = 103,000
Recall that
and
for all
. So


For
, we expect both
and
(i.e. the sine and cosine of any angle that lies in the first quadrant must be positive). By definition of absolute value,
if
.
So we have

making H the answer.
C is always true, because the inequality reduces to x > y.