Question Video: Finding the Value of the Inverse of a Function Using the Arrow Diagram Mathematics

Video Transcript

The figure below represents the function 𝑓 from 𝑥 to 𝑦. Find the value of the inverse of 𝑓 of four.

The function 𝑓 of 𝑥 consists of four ordered pairs: four, 13; six, seven; eight, 10; and 10, four. We know that for the inverse of a function, the output becomes the input and vice versa. This means that the inverse of 𝑓 of 𝑥 consists of the four ordered pairs: 13, four; seven, six; 10, eight; and four, 10. The 𝑥- and 𝑦-values swap.

We’re trying to find the value of the inverse of 𝑓 of four. This means that the 𝑥-value in the ordered pair of the inverse of 𝑓 of 𝑥 must be four. The 𝑦-value that corresponds to this is 10. The inverse of 𝑓 of four is therefore equal to 10. Alternatively, we could’ve found this value from the figure. The 𝑦-value of four corresponds to the 𝑥-value of 10 in the figure. This means that the inverse of 𝑓 of four must be equal to 10.