Given the function f(x) = 6 (x + 2) - 3, solve for the inverse function when x = 21.

Solution:

It is given that

f(x) = 6 (x + 2) - 3

It can be written as

f(x) = 6x + 12 - 3

f(x) = 6x + 9

In order to find the inverse,

consider y = f(x)

y = 6x + 9

Let us interchange x and y,

x = 6y + 9

By solving for y,

x - 9 = 6y

Divide both sides by 6,

x/6 - 9/6 = y

So we get

y = 1/6 x - 3/2

So the inverse function f^-1 (x) = 1/6 x - 3/2

When x = 21

f^-1 (21) = 1/6 (21) - 3/2

Taking LCM

f^-1 (21) = 21/6 - 3/2

f^-1 (21) = (42 - 18)/12

f^-1 (21) = 24/12

f^-1 (21) = 2

Therefore, the inverse function when x = 21 is 2.

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Given the function f(x) = 6 (x + 2) - 3, solve for the inverse function when x = 21.

Summary:

The inverse function f(x) = 6 (x + 2) - 3 when x = 21 is 2.