Given f(x) = 2x and g(x) = x + 3, find fg(2).

Using the same functions f(x) = 2x and g(x) = x + 3, find gf(2).

Find the inverse function f⁻¹(x) where f(x) = x + 5.

Find the inverse function f⁻¹(x) where f(x) = 3x.

If f(x) = x², find ff(3).

Find an expression for fg(x) where f(x) = 2x + 1 and g(x) = x².

Find the inverse of f(x) = (x/3) - 2.

Given f(x) = 2x + 1 and g(x) = x², solve fg(x) = 19.

Find the inverse of f(x) = √(x - 3).

Given f(x) = 1/x, show that ff(x) = x.

Find the inverse of f(x) = (2x + 1)/(x - 3).

Given f(x) = 3x - 2 and g(x) = x², solve the equation f⁻¹(x) = g(x).

Find the composite function fg(x) where g(x) = 1/x and f(x) = (x + 1)/x. Simplify fully.

Given f(x) = (2x - 1)/(x + 3), find f⁻¹(0).

PROOF: Given f(x) = 2x + 1 and g(x) = 3x - 2, show that (fg)⁻¹(x) = g⁻¹f⁻¹(x).