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 one 'undoes' the effect of the other. Graphically, their graphs are reflections of each other across the line $$y = x. $$Step 2: Identify the given functions on the graph. The orange and blue curves represent the two functions, and the dashed line $$y = x is $$the line of reflection for inverse functions. Step 3: Check if the graphs are symmetric with respect to the line $$y = x. $$This means that for every point $$(a, b) on $$one function, there should be a corresponding point $$(b, a) on $$the other function. Step 4: Observe the points where the orange and blue curves intersect the line $$y = x. If $$these points match and the curves are mirror images across this line, the functions are inverses. Step 5: Conclude based on the symmetry. If the orange and blue graphs are reflections of each other across the line $$y = x$$, then the functions are inverses; otherwise, they are not.

Determine whether each pair of functions graphed are inverses.

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Key Concepts

Inverse Functions

Line of Symmetry y = x

Graphical Verification of Inverses