Proving Equivalence of f(x) and g(x)

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The functions f(x) and g(x) are analyzed for equivalence. The function f(x) simplifies to 3x² + 5x - 7, while g(x) simplifies to 3x² + 3x - 7. Since the coefficients of the x terms differ, f(x) and g(x) are not equivalent. The proof demonstrates that while both functions are quadratic, their linear components are distinct, confirming their non-equivalence.

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Consider the two functions f(x)=(x²+3x+10)+(2x²+2x-17) and g(x)=(4x²+4x+4)-(x²+x+11). If they are equivalent, prove they are; if they are not equivalent, prove they aren't.
 
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The first function can be simplified by adding like terms: [math]f(x) = 3x^2 + 5x - 7[/math]. Do the same for g(x). Do they come out the same?

-Dan
 
pappoelarry said:
Consider the two functions f(x)=(x²+3x+10)+(2x²+2x-17) and g(x)=(4x²+4x+4)-(x²+x+11). If they are equivalent, prove they are; if they are not equivalent, prove they aren't.
f(x)=(x²+3x+10)+(2x²+2x-17)= (x^2+ 2x^2)+ (3x+ 2x)+(10- 17)
Can you finish that ?

g(x)=(4x²+4x+4)-(x²+x+11)= (4x^2- x^2)+ (4x- x)+ (4- 11)
Can you finish that?

Are they the same?
 

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