Determine algebraically whether f(x)=(2x+1)/(x-4) is one-to-one.

demitereur 2022-09-18 Answered
Determine algebraically whether f ( x ) = 2 x + 1 x 4 is one-to-one.
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Answers (1)

moderrockblog09
Answered 2022-09-19 Author has 7 answers
Solution:
Given f ( x ) = 2 x + 1 x 4
To show that f is 1-1, you could show that
f ( x ) = f ( y ) x = y 2 x + 1 x 4 = 2 y + 1 y 4 ( 2 x + 1 ) ( y 4 ) = ( 2 y + 1 ) ( x 4 ) 2 x y 8 x + y 4 = 2 x y 8 y + x 4 8 x x = 8 y y x = y
So f(x) is one-to-one

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