Question

`y+ (13)/(4) = (x^2- (1)/(2) )^2`

Answer 1

Answer:
`\bold{y=(1\pm √(4x+13))/(2)}`

Explanation:

Inverse is when you swap the x's and y's and solve for y:

`y+(13)/(4)=\bigg(x-(1)/(2)\bigg)^2\\\\\\x+(13)/(4)=\bigg(y-(1)/(2)\bigg)^2\rightarrow \text{(swapped the x's and y's)}\\\\\\\sqrt{x+(13)/(4)}=\sqrt{\bigg(y-(1)/(2)\bigg)^2}\rightarrow \text{(took square root of both sides)}\\\\\\\sqrt{(4x+13)/(4)}=\pm \bigg(y-(1)/(2)\bigg)}\rightarrow \text{(created common denominator in radical)}\\\\\\ (√(4x+13))/(2)=\pm \bigg(y-(1)/(2)\bigg)}\rightarrow \text{(simplified radical)}`

`\pm (√(4x+13))/(2)=y-(1)/(2)}\rightarrow \text{(divided both sides by}\ \pm )\\\\\\(1)/(2)\pm (√(4x+13))/(2)=y\quad \rightarrow \text{(added}\ (1)/(2)\ \text{to both sides)}\\\\\\(1\pm √(4x+13))/(2)=y\quad \rightarrow \text{(combined numerators)}`