SOLUTION: Which of the following functions, if any, is an odd function? A) f(X)=3X^2+5 B) f(X)= absolute value of (X-2) C) f(X)=cos(X)+7

Algebra ->  Functions -> SOLUTION: Which of the following functions, if any, is an odd function? A) f(X)=3X^2+5 B) f(X)= absolute value of (X-2) C) f(X)=cos(X)+7      Log On


   

Question 1197707: Which of the following functions, if any, is an odd function?
A) f(X)=3X^2+5
B) f(X)= absolute value of (X-2)
C) f(X)=cos(X)+7
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
A function f(x) is odd if -f(x)=f(-x) for all values of x.
a) f%28-x%29=3%28-x%29%5E2%2B5=3x%5E2%2B5=f%28x%29
Since f(-x) does not equal -f(x), it is not odd.
b) f%28-x%29=abs%28-x-2%29 and -f%28x%29=-abs%28x-2%29
abs%28-x-2%29 does not equal -abs%28x-2%29, so it is not odd.
c) f%28-x%29=cos%28-x%29%2B7=cos%28x%29%2B7=f%28x%29
f(-x) does not equal -f(x), so it is not odd.
Therefore, none of the three functions are odd.