Question

Which function has an inverse that is also a function? g(x) = 2x – 3 k(x) = –9x2 f(x) = |x 2| w(x) = –20.

Answer 1

The function has an inverse that is also a function is g(x) = 2x – 3.

The correct option is A.

We have to determine

Which function has an inverse that is also a function?

Inverse function;

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.

1. Here g(x) = 2x - 3 has inverse x = 2y - 3 which simplifies to;

$\rm y = \dfrac{(x-3)}{2}$

This is a line and is a function;

$\rm y = \dfrac{1}{2} x - \dfrac{3}{2}$

2. k(x) = -9x^2 has the inverse x = -9y^2 which simplifies to;

$\rm y=\sqrt{\dfrac{x}{-9}}$

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.

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