f(x) = (4x + 1) /3
f⁻¹ (x ) is the inverse function of x.
Let f(x) = y, x = f⁻¹(y)
f(x) = (4x + 1) /3
y = (4x + 1) /3 Solve for x.
3y = 4x + 1
3y - 1 = 4x Divide both sides by 4
(3y - 1)/4 = x
x = (3y - 1)/4 Recall x = f⁻¹(y)
f⁻¹(y) = (3y - 1)/4
f⁻¹(3) = (3*3 - 1)/4
= (9 - 1)/4 = 8 / 4 = 2
f⁻¹(3) = 2.
I hope this helps.