(30pts)(i need it quick)find the inverse of the given function:

Rewrite your function in terms of x and y. Then solve for y in terms of x:

y = -1/2 * (sqrt(x+3)

-2y = sqrt(x+3)

4y^2 = x +3

x = 4y^2-3

Now swap x and y.

y = 4x^2-3

So you got the correct answer. To determine the domain, look back at the original function:

y = -1/2 * (sqrt(x+3), x ≥ -3

We see that x must be greater or equal to -3 in order for the square root to be a real number. Thus sqrt(x+3) must be nonnegative, by that I mean positive or zero.

So if that part of our function is positive and then we are multiplying it by -1/2, our function will only output a nonpositive number, by that I mean either negative or zero. That means our range for this function is y ≤ 0.

And by definition of the inverse, the range of the original function becomes the domain of the inverse. That means the domain of our inverse is x ≤ 0.

I hope that makes sense!

the equivalent expression are always the hardest ones but you look at the gcf also

step-by-step explanation: