Answer:
Option D is correct.
Step-by-step explanation:
Given equation is \(5y+4=(x+3)^2+\frac{1}{2}\)
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.
\(5y+4=(x+3)^2+\frac{1}{2}\)
\(5y+4-\frac{1}{2}=(x+3)^2\)
\(5y+\frac{7}{2}=(x+3)^2\)
\(\pm\sqrt{5y+\frac{7}{2}}=x+3\)
\(x+3=\pm\sqrt{5y+\frac{7}{2}}\)
\(x=-3\pm\sqrt{5y+\frac{7}{2}}\)
Inverse of the given equation = \(-3\pm\sqrt{5y+\frac{7}{2}}\)
Therefore, Option D is correct.
