Answer:
f⁻¹(19) = 1
Explanation:
We have given a function.
f(x)= 5(x+4) -6
We have to find the inverse function when x = 19.
f⁻¹(x) = ? and f⁻¹(19) = ?
Putting f(x) = y in given function, we have
y = 5(x+4)-6
Separating x from above equation, we have
(y+6)/5 = x+4
(y+6)/5 -4 = x
Swapping above equation, we have
x = (y+6)/5-4
x = y+6-20 / 5
x = y-14 / 5
Putting x = f⁻¹(y) in above equation, we have
f⁻¹(y) = y-14/5
f⁻¹(x) = x-14/5
Putting x= 19 in above equation , we have
f⁻¹(19) =19-14/5
f⁻¹(19) = 5 / 5
f⁻¹(19) = 1 which is the answer.