Question

Max used these steps to find the inverse of function f step number function step description step 1 given step 2 change f() to y step 3 switch x and y f(x) = 5/6 ✕ x - 1/6; y = 5/6 ✕ x - 1/6; x = 5/6 ✕ y - 1/6; x 1/6 = 5/6 ✕ y; 5/6 ✕ x 5/36 = y; 5/6 ✕ x 5/36 = f ⁻ 1 ✕ (x) step 4 step 5 add to each side 1/6 multiply each side by 5/6 replace y with f ⁻ 1 ✕ (x) step 6 use this information to complete the statement max made a mistake in step 5 he should have?

What should Max have done differently in step 5 to correctly find the inverse of the function f?

A) Added 5/6 to each side and multiplied each side by 6/5

B) Subtracted 1/6 from each side and multiplied each side by 6/5

C) Added 1/6 to each side and multiplied each side by 5/6

D) Subtracted 5/6 from each side and multiplied each side by 6/5

Answer 1

Max made an error in step 5 while finding the inverse function. He should have added 1/6 to both sides of the equation and then multiplied each side by 6/5 to isolate y. The correct choice was option B) Subtracted 1/6 from each side and multiplied each side by 6/5.

Step-by-step explanation:

In step 5, Max should have realized that when switching x and y in the function f(x) = 5/6 × x - 1/6, he was not quite finished with the process to solve for the inverse function. After swapping x and y to get x = 5/6 × y - 1/6, he should have isolated y on one side of the equation. To do so correctly, he first needed to add 1/6 to both sides to undo the subtraction of 1/6 from y, and then multiply each side by 6/5 to undo the multiplication of y by 5/6. The correct steps would be:

Add 1/6 to both sides: x + 1/6 = 5/6 × y.

Multiply each side by 6/5 to solve for y: (6/5) × (x + 1/6) = y.

Therefore, Max should have chosen option B) Subtracted 1/6 from each side and multiplied each side by 6/5 to correctly find the inverse of the function f.