Question

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Answer 1

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:

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