Are My Math Solutions Correct?

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The discussion revolves around verifying math solutions and understanding the definition of a function. The user evaluates g(x) = x^2 + x at g(x + 3) and initially provides an incorrect answer of x^2 + 7x - 12, later questioning why the correct answer includes -12. There is a debate about whether certain equations represent functions, with the user asserting that x^2 = y - 3 is not a function, while y^2 = x - y is considered a function. Participants emphasize the importance of understanding the definition of a function to clarify these distinctions. The user expresses gratitude for the insights gained regarding function definitions.
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Hi i am new here, and just wondering if my answers are right, please check for me.

1. Evaluate g(x) = x^2 + x
g(x + 3)
my answer: x^2 + 7x -12

2. Function or not:
x^2 = y - 3
I say not a function.

3. y^2 = x - y
I would say yes this is a function.

thanks a lot
 
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1. why minus 12 and not plus 12?

2. x(y) is not a function but y(x) is a function.

3. x(y) is a function. Although you cannot re-write this expression as a function y of x, you can see from the graph of x(y) that to each x correspond two different y. This means, by the definition of a function that y(x) is not a function.

reply if you want further explanations.
 
2. WHY would you say it is not a function?

3. WHY would you say it is a function?

Crucial to answering both those questions: what is the DEFINITION of "function"?
 
for the first one I figured it out to plus 12 also, but when I check the solution it is -12, so i guess the book is wrong. I understand about function now thanks
 
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