Question

Which function has an inverse that is also a function?

Answer 1

Answer:

g(x) = 2x - 3

Step-by-step explanation:

The inverse of a function is the equation where x and y have switched places. If when you solve for y again, the function passes the vertical line test, the inverse if a function.

g(x) = 2x - 3 has inverse x = 2y - 3 which simplifies to y = (x-3)/2. This is a line and is a function y = 1/2 x - 3/2.

k(x) = -9x^2 has the inverse x = -9y^2 which simplifies to $y = \sqrt{\frac{x}{-9} }$. This is a function but only for certain values of x.

f(x) = |x+2| is an absolute value function. All absolute value functions do not have inverses which are functions.

w(x) = -20 does not have an inverse which is a function.

This means A is the solution.