Answer:
[tex]f^{-1}(x) = 4x^{2}-3, for x\leq -3[/tex]
Step-by-step explanation:
The given equation is ,
[tex]f(x) = y = (\frac{-1}{2})(\sqrt{x+3} )[/tex]
For finding the inverse, we write the equation of x as function of y, and then rewrite replacing x with y and y with x.
Thus, the equation formed is inverse of the given equation.
[tex]f(x) = y = (\frac{-1}{2})(\sqrt{x+3} )[/tex]
[tex](-2)y = (\sqrt{x+3} )[/tex], squaring both the sides.
[tex]4y^{2}=x+3[/tex]
[tex]x = 4y^{2}-3[/tex], now replace x with y and y with x.
Thus, [tex]y = 4x^{2}-3[/tex], where x [tex]\leq[/tex] -3.
