Find the inverse function of f. f(x) = 2 − 6x f −1(x) =

Question

A table of values for a one-to-one function is given. Find the indicated value.

x	1	2	3	4	5	6
f(x)	0	2	3	6	4	1

f(f ⁻¹(6)) = 

Find the inverse function of f.

f(x) = 6x³ + 5

f⁻¹(x) = 

 Find the inverse function of f.

f(x) = 1/x +3

f⁻¹(x) = 



Answer 1

f(f^-1(100)) = 100, f(f-¹(-12)) = -12, f(f^-1(a)) = a, f(f^-1(π) = π

The "f" and the "f^-1" wipe each other out and you just get what you started with.

If you want to use the table, f(4) = 6 therefore f^-1(6) = 4 then to find f(f^-1(6)) we take f(4) to get 6.

To find an inverse function:

Step 1, replace f(x) with "y"

f(x) = 6x³ + 5 becomes y = 6x³ + 5

Step 2: swap places of the "x" and "y"

So y = 6x³ + 5 becomes x = 6y³ + 5

Step 3: solve for "y":

x = 6y³ + 5

x - 5 = 6y³

(x - 5)/6 = y³

y = cuberoot[(x - 5)/6]

Step 4: replace "y" with "f^-1(x)"

y = cuberoot[(x - 5)/6] becomes f^-1(x) = cuberoot[(x - 5)/6]

Do the same for the last problem

Answer 2