Answer:
Option D is correct.
Step-by-step explanation:
Given equation is [tex]5y+4=(x+3)^2+\frac{1}{2}[/tex]
We need to find inverse of the function.
Let x be the independent variable or the function is in x variable.
So,
we Simplify the given equation for variable of x.
[tex]5y+4=(x+3)^2+\frac{1}{2}[/tex]
[tex]5y+4-\frac{1}{2}=(x+3)^2[/tex]
[tex]5y+\frac{7}{2}=(x+3)^2[/tex]
[tex]\pm\sqrt{5y+\frac{7}{2}}=x+3[/tex]
[tex]x+3=\pm\sqrt{5y+\frac{7}{2}}[/tex]
[tex]x=-3\pm\sqrt{5y+\frac{7}{2}}[/tex]
Inverse of the given equation = [tex]-3\pm\sqrt{5y+\frac{7}{2}}[/tex]
Therefore, Option D is correct.
