find f "circle" g and g "circle" f.?

Question

by letting f(x)={x, x<0 and 2x, x> or =0 and g(x)={-3x, x<0 and 5x, x> or =0

Answer 1

fOg (x) = f(g(x)) = f(-3x) if x<0 and f(5x) if x >=0

if x<0, -3x > 0 so fOg (x) = f(-3x) = -3x
if x>0, 5x > 0 so fOg (x) = f(5x) = 5x

gOf(x) = g(f(x))

if x<0
gOf(x) = g(x) = -3x

if x > 0
gOf(x) = g(2x) = 10x

Answer 2

If x < 0 then
f(g(x)) = f(-3x), but since x < 0 we know -3x >0, so the second part of the f(x) definition applies:
f(g(x)) = 2*(-3x)
= -6x

If x > or = 0 then
f(g(x)) = f(5x)
= 2*5x
= 10x

Same idea for gof:

If x < 0 then
g(f(x)) = g(x) and you can finish it yourself from there, remembering that x < 0, then do it for x > 0

Answer 3

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RE:
find f "circle" g and g "circle" f.?
by letting f(x)={x, x<0 and 2x, x> or =0 and g(x)={-3x, x<0 and 5x, x> or =0

Answer 4

fog(x)=f{g(x)}=f(-3x) if x<0 and f(5x) if x>or=0
=-3x if x<0 and 2(5x) if x>or=0
=-3x if x<0 and 10x if x>or=0

gof(x)=g{f(x)}=g(x) if x<0 and g(2x) if x>or=0
=-3x if xor=0
=-3x if x<0 and 10x if x>or=0