SOLUTION: True or false: if f is an odd function whose domain is the set of real numbers and a function g is defined by g(x)={f(x) if x>=0, -f(x) if x<0, then g is an even function. E

Algebra ->  Functions -> SOLUTION: True or false: if f is an odd function whose domain is the set of real numbers and a function g is defined by g(x)={f(x) if x>=0, -f(x) if x<0, then g is an even function. E      Log On


   

Question 941314: True or false: if f is an odd function whose domain is the set of real numbers and a function g is defined by
g(x)={f(x) if x>=0, -f(x) if x<0,
then g is an even function. Explain your answer
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
By definition, an odd function is defined as
f%28-x%29=-f%28x%29
So then if g(x) is defined as -f%28x%29 when x%3C0, then
g%28x%29=-%28-f%28x%29%29 when x%3C0 or
g%28x%29=f%28x%29
which is the definition of an even function.