The function has an inverse that is also a function is g(x) = 2x – 3.
The correct option is A.
<h3>Inverse function;</h3>
The inverse of a function is the equation where x and y have switched places.
We have to determine
Which function has an inverse that is also a function?
If when you solve for y again, the function passes the vertical line test, the inverse if a function.
1. Here g(x) = 2x - 3 has inverse x = 2y - 3 which simplifies to;
![\rm y=\dfrac{(x-3)}{2}](https://tex.z-dn.net/?f=%5Crm%20y%3D%5Cdfrac%7B%28x-3%29%7D%7B2%7D)
This is a line and is a function;
![\rm y=\dfrac{1}{2}x-\dfrac{3}{2}](https://tex.z-dn.net/?f=%5Crm%20y%3D%5Cdfrac%7B1%7D%7B2%7Dx-%5Cdfrac%7B3%7D%7B2%7D)
2. k(x) = -9x^2 has the inverse x = -9y^2 which simplifies to;
![\rm y=\sqrt{\dfrac{x}{-9}}](https://tex.z-dn.net/?f=%5Crm%20y%3D%5Csqrt%7B%5Cdfrac%7Bx%7D%7B-9%7D%7D)
This is a function but only for certain values of x.
3. f(x) = |x+2| is an absolute value function.
All absolute value functions do not have inverses which are functions.
4. w(x) = -20 does not have an inverse which is a function.
Hence, the function has an inverse that is also a function is g(x) = 2x – 3.
To know more about inverse function click the link given below.
brainly.com/question/20663378