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Stells [14]
3 years ago
6

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

Mathematics
1 answer:
lisov135 [29]3 years ago
4 0

Answer:  14

<u>Step-by-step explanation:</u>

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

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