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)

Explanation:

Step1: Recall inverse function property

If \((a, b)\) is on \(f^{-1}(x)\), then \((b, a)\) is on \(f(x)\).

Step2: Identify \(a\) and \(b\)

Given \((-1, 0.5)\) is on \(f^{-1}(x)=2^x\), so \(a = - 1\), \(b = 0.5\).

Step3: Find the point on \(f(x)\)

Using the property, the point on \(f(x)=\log_2x\) should be \((b, a)=(0.5, - 1)\).

Answer:

B. (0.5, -1) (assuming the options are labeled with letters, if not, the point (0.5, -1))