Question

Which statement could be used to explain why fx) = 2x - 3 has an inverse relation that is a function?

The graph of f(x) passes the vertical line test.
f(x) is a one-to-one function
The graph of the inverse of f(x) passes the horizontal line test.
f(x) is not a function.

Answer 1

B. f(x) is a one-to-one function.

Explanation:

Answer 2

f(x) is a One-one function

Explanation:

A function can only have an inverse function if it is one-one.

In order for a function to be one-one it has to pass the horizontal line test.

In other words an equation like f(x) = x^2

If you check the graph of this function you would find that it is in the shape of a parabola. In other words, more than one x-value has the same y-value. For example, x=2 and x= -2. You would find that both values give the same y-value, 4. So in this case f(x) would not pass the horizontal line test and would not be a one-one function, hence not making it an inverse.