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

Step 1: Replace f(x) with y.

y = 3x - 7

Step 2: Interchange x and y.

To find the inverse, switch the roles of the input and output:

x = 3y - 7

Step 3: Solve the equation for y.

Add 7 to both sides:
x + 7 = 3y

Divide both sides by 3:
y = (x + 7)/3

Step 4: Write the result using inverse-function notation.

f⁻¹(x) = (x + 7)/3

Step 5: Check the inverse using composition.

Substitute f⁻¹(x) into f:
f((x + 7)/3) = 3((x + 7)/3) - 7

Simplify:
f((x + 7)/3) = x + 7 - 7
f((x + 7)/3) = x

This confirms the inverse.

Therefore, f⁻¹(x) = (x + 7)/3.