Find the inverse of the given function. f(x)= -1/2SQR x+3, x greater than or equal to -3

Answer:So, the inverse of function [tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex] is [tex]f^{-1}(x)= 4x^2-3[/tex]Step-by-step explanation:We need to find the inverse of the given function[tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex]To find the inverse we replace f(x) with y[tex]y = \frac{-1}{2} \sqrt{x+3}[/tex] Now, replacing x with y and y with x[tex]x = \frac{-1}{2} \sqrt{y+3}[/tex] Now, we will find the value of y in the above equationMultiplying both sides by -2[tex]-2x = \sqrt{y+3}[/tex] Taking square on both sides[tex](-2x)^2 = (\sqrt{y+3})^2[/tex][tex]4x^2 = y+3[/tex]  Finding value of y[tex]y = 4x^2-3[/tex]Replacing y with f⁻¹(x)[tex]f⁻¹(x)= 4x^2-3[/tex]So, the inverse of function [tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex] is [tex]f^{-1}(x)= 4x^2-3[/tex]