Question

If f(x)=3x+2,find f(f^-1(14)).

Answer 1

Answer:  14

Step-by-step explanation:

f(x) = 3x + 2

To find f⁻¹, swap the x's and y's and solve for y --> Note: f(x) is y

x = 3y + 2

x - 2 = 3y

$\dfrac{x-2}{3}=y$

$\implies f^{-1}(x)=\dfrac{x-2}{3}$

$\implies f^{-1}(14)=\dfrac{14-2}{3}$

$\implies f^{-1}(14)=\dfrac{12}{3}$

$\implies f^{-1}(14)=4$

f(f⁻¹(14)) = f(4)

              f(4) = 3(4) + 2

                     = 12 + 2

                     = 14

NOTE: the simplified version is .... f and f⁻¹ cancel out, leaving you with 14