The inverse function of [tex]f(x) = -\frac 12\sqrt{x + 3}[/tex] is[tex]f^{-1}(x) = 4x^2- 3[/tex]
How to determine the inverse function?
The function is given as:
[tex]f(x) = -\frac 12\sqrt{x + 3}[/tex]
Rewrite as;
[tex]y = -\frac 12\sqrt{x + 3}[/tex]
Swap the positions of x and y
[tex]x = -\frac 12\sqrt{y + 3}[/tex]
Multiply through by -2
[tex]-2x = \sqrt{y + 3}[/tex]
Square both sides
4x^2 = y + 3
Subtract 3 from both sides
y = 4x^2 - 3
Express as an inverse function
[tex]f^{-1}(x) = 4x^2- 3[/tex]
Hence, the inverse function of [tex]f(x) = -\frac 12\sqrt{x + 3}[/tex] is[tex]f^{-1}(x) = 4x^2- 3[/tex]
Read more about inverse function at:
https://brainly.com/question/2541698
#SPJ1
