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Mathematics
OpenStudy (anonymous):

Determine whether 8y+7xy= -7x^2 -3 defines y as a function of x. Please show all of your work. Determine whether 8y+7xy= -7x^2 -3 defines y as a function of x. Please show all of your work. @Mathematics

OpenStudy (agreene):

7 x y+8 y = -7 x^2-3 Expand out terms of the left hand side: (7 x+8) y = -7 x^2-3 Divide both sides by 7 x+8: \[y = \frac{-3-7 x^2}{8+7 x}\] while \[8+7x\neq0\]

jimthompson5910 (jim_thompson5910):

\[\Large 8y+7xy= -7x^2 -3\] \[\Large y(8+7x)= -7x^2 -3\] \[\Large y= \frac{-7x^2 -3}{8+7x}\] Since we were able to isolate y cleanly, this means that the original expression is a function (you may have to rearrange terms first, but it's possible to represent it as a function)

OpenStudy (agreene):

Jim is correct, but realise that this function has a hole at x=-8/7

jimthompson5910 (jim_thompson5910):

good point agreene

jimthompson5910 (jim_thompson5910):

so \[\Large x \neq -\frac{8}{7}\]

OpenStudy (anonymous):

Jim- where does this x≠−8/7 go in the above post? At the end?

jimthompson5910 (jim_thompson5910):

yes, after the function definition, you would throw in that condition so it would look something like this \[\Large y = \frac{-7x^2 -3}{8+7x} \ \text{where} \ x \neq -\frac{8}{7}\]

OpenStudy (anonymous):

Great! Thank you so much jim

jimthompson5910 (jim_thompson5910):

np

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