Flipping Functions

Algebra Level 2

Given that f ( x ) = a x + b f( x) =ax+b and f − 1 ( x ) = x − 3 4 f^{ -1 } ( x) =\dfrac { x-3 }{ 4 } , find the value of a b ab .


The answer is 12.

Lee Care Gene by Lee Care Gene , 20, Malaysia

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1 solution

Chew-Seong Cheong
Jun 24, 2016

Let y = f ( x ) = a x + b y = f(x) = ax +b .

⟹ f − 1 ( y ) = y − 3 4 x = y − 3 4 ⟹ y = 4 x + 3 f ( x ) = 4 x + 3 \begin{aligned} \implies f^{-1}(y) & = \frac {y-3}4 \\ x & = \frac {y-3}4 \\ \implies y & = 4x + 3 \\ f(x) & = 4x + 3 \end{aligned}

⟹ a b = 4 × 3 = 12 \implies ab = 4\times 3 = \boxed{12}

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