Question

Define the following functions:
f(x)=|x|
g(x)=|x-3|
f+g and f-g and f*g and f/g and g/f

Answer 1

guys help me plz

Answer 2

we know that |x| =x when x>= 0 ,
and |x|=-x when x<0
similarly, |x-3| = x-3 when x >=3
|x-3| = -(x-3) when x<3
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so we consider these intervals,
x< 0 where |x| = -x and |x-3| = -(x-3)

then f+g = -x-x+3 = -2x+3 in the interval x<0
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next interval is x>=0 but x<=3
here, |x| =x , |x-3| = - (x-3)

here f+g = x- x+3 = 3
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finally last interval is x>3
when both, |x| = x , and |x-3| = x-3

f+g = x+x-3 = 2x-3
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so, in all, your f+g will be ,