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

Given: Function f(x) = 5(x + 4) - 6

An inverse function reverses the operation done by a particular function.

In other words, the inverse function undoes the action of the other function.

First replace f(x) with y.

y = 5(x + 4) - 6

Using the multiplicative distributive property,

y = 5x + 20 - 6

y = 5x + 14

Replace x with y and y with x.

x = 5y + 14

Solving for y, we get,

5y = x - 14

y = (x - 14)/5

Finally replace y with f ^-1(x).

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

Given x = 19,

y = (19 - 14)/5

y = 5/5

y = 1

Verification:

(f ∘ f ^-1)(x)= x

(f ∘ f ^-1)(x)= f [ f ^-1(x)]

= f [(x - 14)/5]

= f [x/5 - 14/5]

= 5[x/5 - 14/5] +14

= x - 14 + 14

= x

Therefore, the inverse function when x = 19 is 1.

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

Summary:

If the function f(x) = 5(x + 4) - 6, then the inverse function when x = 19 is 1.