Question

The point (–1, 0.5) lies on the graph of f –1(x) = 2x. Based on this information, which point lies on the graph of f(x) = log2x? (–0.5, 1) (0.5, –1) (1, –0.5) (1, 0.5)

Answer 1

(0.5, -1)
   f^-1(x) and f(x) are inverse functions of each other. That means that for all x, f^-1(f(x)) = x and f(f^-1(x)) = x. So for f^-1(x) we've been given the point (-1, 0.5) which means that we have an x value of -1 and a y value of 0.5. So if we swap the x and y values, we'll have a valid point for function f(x). Therefore an x value of 0.5 and a y value of -1 will work. So the answer is (0.5, -1). Notice that no math has to be done, you just need to know the meaning of inverse functions.

Answer 2

Answer:

C. (0.5, -1)

Step-by-step explanation:

This is the correct answer on ed-genuity.

The function $f^{-1} (x)$ is the inverse of the function $f(x)$. So, to find what point of the four lies on the graph of $f(x)$, simply switch the x and y values of the $f^{-1} (x)$ point that they gave you, which would give you your answer of (0.5, -1).

Hope this helps! :)