Question

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

Answer 1

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
\[8+7x\neq0\]

Answer 2

\[\Large 8y+7xy= -7x^2 -3\]



\[\Large y(8+7x)= -7x^2 -3\]


\[\Large y= \frac{-7x^2 -3}{8+7x}\]


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)

Answer 3

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

Answer 4

good point agreene

Answer 5

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

Answer 6

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

Answer 7

yes, after the function definition, you would throw in that condition


so it would look something like this



\[\Large y = \frac{-7x^2 -3}{8+7x} \ \text{where} \ x \neq -\frac{8}{7}\]

Answer 8

Great! Thank you so much jim

Answer 9

np