11. If f (x) = 4x-9, what is the equation for f^-1 (x) ?

F (x) = 4x - 9

let f (x) = y, this implies that x = f⁻¹ (y)

y = 4x - 9 Let us solve for x.

4x - 9 = y

4x = y + 9

x = (y + 9) / 4

Recall that x = f⁻¹ (y),

x = (y + 9) / 4

f⁻¹ (y) = (y + 9) / 4

That means that for f⁻¹ (x)

f⁻¹ (x) = (x + 9) / 4

Hope this explains it.