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dybincka [34]
3 years ago
11

Help pleasesince you guys like to delete my questions for no reason

Mathematics
1 answer:
Basile [38]3 years ago
6 0

Answer:

Option C: \displaystyle y = -3 \pm \sqrt{5 x + \frac{7}{2}.

Step-by-step explanation:

Typically, solving an equation means finding an expression of y that is written in x. However, this question is asking for the inverse of an equation in an x-y plane. Thus, start by solving for an expression of x that is written in y. After that, interchange x and y to obtain the equation of the inverse.

\displaystyle 5 y + 4 = (x + 3)^{2} + \frac{1}{2}.

\displaystyle (x + 3)^{2} + \frac{1}{2} = 5 y + 4.

Subtract 1/2 from both sides of this equation:

\displaystyle (x + 3)^{2} = 5 y + \frac{7}{2}.

Take the square root of both sides of this equation; note the plus-minus sign on the right-hand side of this equation:

\displaystyle (x + 3) = \pm(\5 y + \frac{7}{2}).

Subtract 3 from both sides of this equation:

\displaystyle x = -3 \pm(\5 y + \frac{7}{2}).

Interchange x and y to obtain the equation for the inverse:

\displaystyle y = -3 \pm(\5 x + \frac{7}{2}).

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Answer

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Questions can be asked through comment.

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