Inverse Function

Algebra Level 1

If f ( x ) = 16 x + 3 f(x) = 16x + 3 , what is the value of f − 1 ( 3 ) f^{-1}(3) ?


The answer is 0.

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Raihan Fauzan by Raihan Fauzan , 20, Indonesia

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3 solutions

Viki Zeta
Oct 16, 2016

Relevant wiki: Inverse Functions

f ( x ) = 16 x + 3 To get f − 1 ( x ) just change x to f − 1 and f(x) to x x = 16 f − 1 ( x ) + 3 x − 3 = 16 f − 1 ( x ) f − 1 ( x ) = x − 3 16 f − 1 ( 3 ) = 3 − 3 16 = 0 16 = 0 f(x) = 16x + 3 \\ \text{To get }f^{-1}(x) \text{ just change x to }f^{-1} \text{ and f(x) to x} \\ x = 16f^{-1}(x) + 3 \\ x- 3 = 16f^{-1}(x) \\ f^{-1}(x) = \dfrac{x-3}{16} \\ f^{-1}(3) = \dfrac{3-3}{16} = \dfrac{0}{16} = 0

7 Helpful 2 Interesting 0 Brilliant 2 Confused

Thank you...

Raihan Fauzan - 4 years, 8 months ago
Raihan Fauzan
Oct 16, 2016

Relevant wiki: Inverse Functions

f ( x ) = y = 16 x + 3 f(x) = y = 16x + 3

f − 1 ( y ) = x = y − 3 16 f^{-1}(y) = x = \frac{y - 3}{16}

f − 1 ( x ) = x − 3 16 f^{-1}(x) = \frac{x - 3}{16}

f − 1 ( 3 ) = 3 − 3 16 = 0 f^{-1}(3) = \frac{3 - 3}{16} = \boxed{0}

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Gia Hoàng Phạm
Nov 24, 2018

Relevant wiki: Inverse Functions

f − 1 ( 3 ) = x ⟹ f ( x ) = 3 ⟹ 16 x + 3 = 3 ⟹ 16 x = 0 ⟹ x = 0 f^{-1}(3)=x \implies f(x)=3 \implies 16x+3=3 \implies 16x=0 \implies x=0

1 Helpful 0 Interesting 0 Brilliant 0 Confused

That’s how I solved it too!

Vincent Lancaster - 1 month, 1 week ago

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