Question

Please please help!!!

Answer 1

Answer:$f^{-1}(x)=4x^{2} -3, x\leq 0$

Step-by-step explanation:The inverse of a function is a function that reverses the given function. Imagine a function as a little machine that turns one number into another. the new machine(inverse) will do the reverse of this process. In mathematics you do this by isolating the variable. Like this:

$y=-\frac{1}{2} \sqrt[2]{x+3} \\(-2)y=\sqrt[2]{x+3}\\((-2)y)^{2} =]{x+3}\\4y^{2} ={x+3}\\4y^{2}-3 =x\\\\f^{-1}(x)=4x^{2} -3, x\leq 0$

Now the domain of the inverse function will be the range of the original function. In this excercise the range will always be negative so the domain of the inverse shall be the same