Answer:
[tex]\huge\boxed{f^{-1}(x) = \frac{7x-5}{3}}[/tex]
Step-by-step explanation:
Given the function:
[tex]f(x) = \frac{3x+5}{7}[/tex]
Put f(x) = y
[tex]y = \frac{3x+5}{7}[/tex]
Interchange x and y
[tex]x = \frac{3y+5}{7}[/tex]
Solve for y
[tex]x = \frac{3y+5}{7}[/tex]
Multiplying both sides by 7
[tex]7x = 3y+5[/tex]
Subtracting y to both sides
[tex]7x-5 = 3y[/tex]
Dividing both sides by 3
[tex]\frac{7x-5}{3} = y[/tex]
OR
[tex]y = \frac{7x-5}{3}[/tex]
Put y = [tex]f^{-1}(x)[/tex]
So,
[tex]f^{-1}(x) = \frac{7x-5}{3}[/tex]
Hope this helped!
~AnonymousHelper1807
