Question

what is the inverse of the logarithmic function \\(f(x) = \log_2 x\\)?

\\(f^{-1}(x) = x^2\\)
\\(f^{-1}(x) = 2^x\\)
\\(f^{-1}(x) = \log_x 2\\)
\\(f^{-1}(x) = \frac{1}{\log_2 x}\\)

the point \\((-1, 0.5)\\) lies on the graph of \\(f^{-1}(x) = 2^x\\). based on this information, which point lies on the graph of \\(f(x) = \log_2 x\\)?

\\((-0.5, 1)\\)
\\((0.5, -1)\\)
\\((1, -0.5)\\)
\\((1, 0.5)\\)

Explanation:

Find the inverse function

Using the Logarithmic and Exponential Inverses knowledge point

$$
LATEXBLOCK0
$$

Find the corresponding point on the original graph

Using the Inverse Functions knowledge point

$$
LATEXBLOCK1
$$

Answer:

Question 1

• (A) \(f^{-1}(x) = x^2\)
• (B) \(f^{-1}(x) = 2^x\) (Correct answer)
• (C) \(f^{-1}(x) = \log_x 2\)
• (D) \(f^{-1}(x) = \frac{1}{\log_2 x}\)

Question 2

• (A) \((-0.5, 1)\)
• (B) \((0.5, -1)\) (Correct answer)
• (C) \((1, -0.5)\)
• (D) \((1, 0.5)\)