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# Given the function f(x) = 4(x + 3) - 5, solve for the inverse function when x = 3.

**Solution:**

An inverse function reverses the operation done by a particular function. In other words, the inverse function undoes the action of the other function.

Given: Function is f(x) = 4(x + 3) - 5

First replace f(x) with y.

⇒ y = 4(x + 3) - 5

Using the multiplicative distributive property

⇒ y = 4x + 12 - 5

⇒ y = 4x + 7

Next replace x with y and y with x.

⇒ x = 4y + 7

Solving for y, we get,

⇒ 4y = x - 7

⇒ y = (x - 7)/4

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

⇒ f ^{-1}(x) = (x - 7)/4

Given x = 3,

y = (3 - 7)/4

y = -4/4

y = -1

**Verification:**

(f ∘ f ^{-1})(x)= x

(f ∘ f ^{-1})(x)= f [f ^{-1}(x)]

= f [(x - 7)/4]

= f [x/4 - 7/4]

= 4[x/4 - 7/4] +7

= x - 7 + 7

= x

Therefore, the inverse function when x = 3 is -1.

## Given the function f(x) = 4(x + 3) - 5, solve for the inverse function when x = 3.

**Summary:**

If the function f(x) = 4(x + 3) - 5, then the inverse function when x = 3 is -1.

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