Given the function f(x) = 5(x + 4) - 6, solve for the inverse function when x = 19.
72, 1, 84, 68

Solution:

Given Function f(x) :

 5(x + 4) - 6

f(x) = 5x + 14

Let f(x) = y

⇒ y = 5x + 14

On interchanging the variables,

⇒ x = (y - 14)/ 5

If f(x) = y, x = f ^-1(y)

f ^-1(y) = (y - 14)/5

f ^-1(x) = (x - 14)/ 5

Inverse function f ^-1(x) = (x - 14)/ 5

Inverse function when x = 19 is

f ^-1(19) = (19 - 14)/ 5

f ^-1(19) = 5/5 = 1

Hence, 2nd option is the correct answer.

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

Summary:

Given the function f(x) = 5(x + 4) - 6, for the inverse function when x = 19, f^-1(x) is 1. Hence, second option is the correct answer.