Answer:
[tex][/tex]
Explanation:
Given:
2(x - 2)² = 8(7+ y)
To find:
the inverse of the function
To determine the inverse, first we need to make y the subject of the formula:
[tex]\begin{gathered} 2\left(x-2\right)²=8\left(7+y\right) \\ 2\left(x-2\right)²=56\text{ + 8y} \\ 2\left(x-2\right)²\text{ - 56}=8y \\ y\text{ = }\frac{2(x\text{ - 2\rparen}^2-\text{ 56}}{8} \\ y\text{ = }\frac{(x\text{ - 2\rparen}^2}{4}\text{ - 7} \end{gathered}[/tex]
Next, interchange x and y:
[tex]\begin{gathered} x\text{ = }\frac{(y-2)^2}{4}-\text{ 7} \\ \\ Then,\text{ }make\text{ y the subject of the formula:} \\ x\text{ + 7 = }\frac{(y-2)^2}{4} \\ 4(x\text{ + 7\rparen= \lparen y - 2\rparen}^2 \\ 4x\text{ + 28 = \lparen y - 2\rparen}^2 \end{gathered}[/tex][tex]\begin{gathered} Square\text{ root both sides:} \\ \pm\sqrt{4x\text{ + 28}}\text{ = }\sqrt{(y-2)^2} \\ y\text{ - 2 = }\pm\sqrt{4x\text{ + 28}} \\ y\text{ = 2 }\pm\sqrt{4x\text{ + 28}} \\ \\ y\text{ = 2 }\pm\sqrt{28\text{ + }4x}\text{ \lparen last option\rparen } \end{gathered}[/tex]
