Question

if f is an even function, determine if g is even, odd or neither. Explain
a) g(x)=-f(x)
b) g(x)=f(-x)
c) g(x)=f(x)-2
d) g(x)=-f(x-2)

Answer 1

if f is even then f(-x) = f(x)

for any function Q, if Q(-x) = Q(x) it is even and if Q(-x) = -Q(x), it is odd.
So my hint is to try replacing x with -x for g(x)

i.e. find g(-x) in each case and then replace any f(-x) that appears with f(x) since f is even.

Answer 2

let's take a look at g(-x)

a) g(-x) = -f(-x).

But since is even, we have f(-x) = f(x), thus, g(-x) = -f(x) = g(x). So g is even

try the others

Answer 3

but since *f* is even...