Question

Given the function f(x)= 5(x+4) -6, solve for the inverse function when x=19.

Answer 1

f(x)= 5(x+4) -6

To find inverse we follow the steps given below

step 1: replace f(x) with y

y= 5(x+4) - 6

step 2: replace x with y and y with x

x= 5(y+4) -6

step 3: solve for y

x= 5(y+4) -6

x + 6 = 5(y+4)

x + 6 = 5y +20

x - 14 = 5y

`(x-14)/(5) = y`

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

`f^(-1)(x) = (x-14)/(5)`

We got the inverse function

solve for the inverse function when x=19.

we replace 19 for x in f^-1(x)

`f^(-1)(19) = (19-14)/(5)`= 1

`f^(-1)(19) =1`