Question

Determine if the following is true or false
a) fog=gof .
b)If f(X) is even function ,then f(x-a) is also even function. please.....

Answer 1

false

Answer 2

both are false in general would you like examples?

Answer 3

for example
\[f(x)=x^2,g(x)=x-2\] then
\[f\circ g = f(g(x))=f(x-2)=(x-2)^2=x^2-4x+4\]
\[g\circ f = g(f(x))=g(x^2)=x^2-2\]

Answer 4

f(x)=sqrt(x) and g(x)=x^2
can be an example for a.

Answer 5

for b) we can also use
\[f(x)=x^2\] which is even , but
\[f(x-2)=x^2-4x+4\] is neither even or odd

Answer 6

i see totally got it thanks a lot