Question

Determine whether each pair of functions graphed are inverses.

Accepted Answer

Step 1: Understand the concept of inverse functions. Two functions are inverses if their graphs are reflections of each other across the line $$y = x. $$This means that every point $$(a, b) on $$one function corresponds to a point $$(b, a) on $$the other function. Step 2: Identify the two functions on the graph. The orange curve represents one function, and the blue curve represents the other function. The green dashed line is the line $$y = x$$, which acts as the mirror line for checking inverses. Step 3: Check if the two functions are symmetric with respect to the line $$y = x. $$Visually inspect if the orange and blue curves are mirror images of each other across the green dashed line. Step 4: Look for corresponding points on the two functions. For example, if the orange function passes through $$(4, 2)$$, then the blue function should pass through $$(2, 4)$$ for them to be inverses. Step 5: Conclude whether the two functions are inverses based on the symmetry and corresponding points. If the graphs are reflections across $$y = x$$, then the functions are inverses; otherwise, they are not.

Determine whether each pair of functions graphed are inverses.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Inverse Functions

Line of Symmetry y = x

Graphical Verification of Inverses