Question: Functions f and g

Comment on Functions f and g

Dear Sir ,

Would Please care to explain the following explanation, which i found in greprep question.


GIVEN y = 5x^2 − 10x + 7y

QUANTITY A -----X QUANTITY B ----- Y

This is an interesting one! There are many tedious ways to solve this one. The one highlighted here is a clever and fast way to solve this kind of questions. Consider the expression (y−x) which it can be derived from the expression of y given, y − x = 5x^2 − 11x + 7 = f(x)

This quadratic function has no real roots since b2−4ac<0 and since a>0 f(x) is always greater than 0 i.e, (y−x)>0 or y>x.
Therefore the correct choice is B.
The correct answer B

Regards
Shubham
greenlight-admin's picture

Are you sure you transcribed the question correctly?

If y = 5x^2 − 10x + 7y, then we can say -6y = 5x^2 − 10x

Or, we can write: y = (5x^2 − 10x)/(-6)
At this point, we can see that when x = 0, y = 0 also
Since it's possible that the two quantities can be equal, the correct answer is either C or D. The answer cannot be B, as you suggest.

Hi Brent, i'm struggling to understand this topic. I've been doing lots of practice problems, but they don't seem to be helping. Do you recommend any tips to help me understand function notation better?
Thanks!
greenlight-admin's picture

You're not alone. In fact, I distinctly remember not like function notation when I first encountered it.

Here are a couple more pages that might help:
- https://mathbitsnotebook.com/Algebra1/Functions/FNNotationEvaluation.html
- https://www.thatquiz.org/tq/previewtest?H/M/M/O/ISMT1391098730

Cheers,
Brent

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