It's asking if we can subtract any two functions and get the same result.
Let's say that f(x) = 2x+5 and g(x) = 7x-10
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Subtracting f-g leads to...
f(x) - g(x) = ( f(x) ) - ( g(x) )
f(x) - g(x) = ( 2x+5 ) - ( 7x-10 )
f(x) - g(x) = 2x+5 - 7x+10
f(x) - g(x) = (2x-7x) + (5+10)
f(x) - g(x) = -5x + 15
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Subtracting in the opposite order leads to...
g(x) - f(x) = ( g(x) ) - ( f(x) )
g(x) - f(x) = ( 7x-10 ) - ( 2x+5 )
g(x) - f(x) = 7x-10 - 2x-5
g(x) - f(x) = (7x-2x) + (-10-5)
g(x) - f(x) = 5x-15
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We see that f-g is not the same as g-f
So generally, function subtraction is not commutative.
This is because subtraction is generally not commutative. Take for example how 7-2 = 5 and 2-7 = -5 are different results. The only time subtraction is commutative is when you're subtracting some number from itself (eg: 7-7 = 0).
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