Function Challenge 4

Algebra Level 2

Consider 2 functions f ( x ) f(x) , g ( x ) g(x) that is defined on the interval [ 0 , ∞ ) [0, \infty) where f ( x ) = x 3 + x 2 + x + 2 f(x)=x^3+x^2+x+2 g ( x ) = 2 f − 1 ( x ) − 1 g(x)=2f^{-1}(x)-1 Find the value of g − 1 ( 0 ) + g − 1 ( 3 ) g^{-1}(0)+g^{-1}(3) .

Note: f − 1 ( x ) f^{-1}(x) is the inverse function of f ( x ) f(x) .

This is one part of 1+1 is not = to 3 .


The answer is 18.875.

Kenneth Tan by Kenneth Tan , 21, Malaysia

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1 solution

展豪 張
Mar 25, 2016

g ( f ( x ) ) = 2 f − 1 ( f ( x ) ) − 1 = 2 x − 1 g(f(x))=2f^{-1}(f(x))-1=2x-1
f ( x ) = g − 1 ( 2 x − 1 ) f(x)=g^{-1}(2x-1)
g − 1 ( 0 ) + g − 1 ( 3 ) = f ( 0.5 ) + f ( 2 ) = 18.875 g^{-1}(0)+g^{-1}(3)=f(0.5)+f(2)=18.875
Proving that f f and g g are bijective is left as an exercise to reader. XDD


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