Question

Help please


since you guys like to delete my questions for no reason

Answer 1

Option C:
`\displaystyle y = -3 \pm \sqrt{5 x + (7)/(2)`.

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) + (1)/(2)`.

`\displaystyle (x + 3)^(2) + (1)/(2) = 5 y + 4`.

Subtract 1/2 from both sides of this equation:

`\displaystyle (x + 3)^(2) = 5 y + (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 + (7)/(2))`.

Subtract
`3` from both sides of this equation:

`\displaystyle x = -3 \pm(\5 y + (7)/(2))`.

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

`\displaystyle y = -3 \pm(\5 x + (7)/(2))`.