Question

if \\((1, -5)\\) is a point on the graph of a one-to-one function \\(f\\), which of the following points is on the graph of \\(f^{-1}\\)?

choose the correct answer below.

\\((-5, 1)\\)
\\((-1, 5)\\)
\\((5, -1)\\)
\\((1, 5)\\)

Explanation:

Identify the given point on the function

Using the One-to-One Function knowledge point

$$ (1, -5) \in \text{graph}(f) \implies f(1) = -5 $$

Apply the definition of an inverse function

Using the Inverse Function Definition knowledge point

$$ f(a) = b \iff f^{-1}(b) = a \implies f^{-1}(-5) = 1 $$

Determine the corresponding point on the inverse graph

Using the Inverse Function Definition knowledge point

$$ f^{-1}(-5) = 1 \implies (-5, 1) \in \text{graph}(f^{-1}) $$

Answer:

• (A) \((-5,1)\) (Correct answer)
• (B) \((-1,5)\)
• (C) \((5,-1)\)
• (D) \((1,5)\)