# If #f(x)=x^2-16#, #g(x)=16-x^2#, how do you find #(f-g)(x)#?

Simply subtract the two functions.

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To find ( (f - g)(x) ), subtract the function ( g(x) ) from the function ( f(x) ) term by term:

[ (f - g)(x) = f(x) - g(x) ]

Given ( f(x) = x^2 - 16 ) and ( g(x) = 16 - x^2 ), substitute these expressions into the subtraction:

[ (f - g)(x) = (x^2 - 16) - (16 - x^2) ]

Now, distribute the negative sign into the parentheses:

[ (f - g)(x) = x^2 - 16 - 16 + x^2 ]

Combine like terms:

[ (f - g)(x) = x^2 + x^2 - 16 - 16 ]

[ (f - g)(x) = 2x^2 - 32 ]

So, ( (f - g)(x) = 2x^2 - 32 ).

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