Question

Determine whether each pair of functions graphed are inverses.

Accepted Answer

Step 1: Understand that two functions are inverses if their graphs are reflections of each other across the line $$y = x. $$This means every point $$(a, b) on $$one function corresponds to a point $$(b, a) on $$the other function. Step 2: Observe the given graph, which shows two functions (one in orange and one in blue) and the line $$y = x ($$green dashed line). The line $$y = x$$ acts as the mirror line for checking inverses. Step 3: Check if the orange and blue graphs are symmetric with respect to the line $$y = x. $$This means visually verifying if the blue graph is the reflection of the orange graph across the green dashed line. Step 4: Notice that the orange graph is on the right side of the $$y-$$axis and the blue graph is on the left side, and they appear to be mirror images across the line $$y = x. $$This suggests they could be inverses. Step 5: Conclude that since the two graphs are reflections of each other across the line $$y = x$$, the pair of functions graphed are inverses of each other.

Determine whether each pair of functions graphed are inverses.

Verified video answer for a similar problem:

Key Concepts

Inverse Functions

Line of Symmetry y = x

Graphical Verification of Inverses