Question

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

Answer 1

Answer: 14

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

`(x-2)/(3)=y`

`\implies f^(-1)(x)=(x-2)/(3)`

`\implies f^(-1)(14)=(14-2)/(3)`

`\implies f^(-1)(14)=(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