Given the function f(x) = 3x - 7.

We need to find the inverse function f^-1 (x).

First we will rewrite.

Let y = 3x - 7.

The goal is to isolate x on one side.

Now we will add 7 to both sides.

==> y + 7 = 3x - 7 + 7

==> y + 7 = 3x

Now we will divide by 3:

==> (y+ 7) /3 = x

==> x = ( y+ 7) /3

Now we will rewrite x as y and y as x:

==> y= (x+ 7) /3

==> Then the inverse of f(x) = (x+ 7) /3

==>** f^-1 ( x) = (x+ 7) /3**

We need to find the inverse formula for the function f(x)= 3x-7

Inverse functions are reflections of the original function over the line y = x. As such, to find the inverse we can switch the x's for the y's like so :

y = 3x - 7 (original)

x = 3y - 7 (inverse)

We want the inverse to be a function of x, not y, so we solve for y:

y = ( x + 7 )/3

To determine the inverse function means to determine x with respect to y, from the given expression of f(x).

We'll note f(x) = y and we'll re-write the equation:

y = 3x - 7

We'll use the symmetryc property:

3x - 7 = y

We'll isolate 3x to the left side. For this reason, we''' add 7 both sides:

3x = y + 7

Now, we'll divide by 3 both sides to get x

x = (y+7)/3

The inverse function is f(y) = (y+7)/3

By definition, we'll write the inverse function as:

f^-1(x) = (x+7)/3

**f^-1(x) = x/3 + 2.(3)**

To find the inverse of f(x) = 3x-7.

Let the inverse of f(x) = 3x-7 be f^-1 (x) = y.

Then by definition, x = f(y).

So x= 3y-7.

We add 1 to both sides and solve for y:

x+7 = 3y.

We divide both sides by 3:

(x+7)/3 = y.

Therefore y = (x+7)/3.

Therefore y = f^-1(x) = (x+7)/3.

Therefore f^-1 (x) = (x+7)/3 is the inverse of f(x) = 3x-7.