If f(x + 2) = 7x + 13, then
f(x) = f((x - 2) + 2)
f(x) = 7 (x - 2) + 13
f(x) = 7x - 1
I'm not sure if you are looking for the value of the inverse at x = 2, or the derivative at x = 2, so I'll just do both.
• If "f¹" means "inverse", then we can either find the inverse explicitly and evaluate it, or solve for x such that f(x) = 2. The latter approach is quicker:
f(x) = 2
7x - 1 = 2
7x = 3
x = 3/7
so f(3/7) = 2, which means f⁻¹(2) = 3/7. (Highlighting this solution because I get the feeling this is the interpretation you want.)
• If "f¹" means "derivative", then differentiating and evaluating gives
f(x) = 7x - 1 ⇒ f'(x) = 7 ⇒ f'(2) = 7