Which of the following functions is one-to-one?

A) $f ( x ) = \lfloor x \rfloor + 2$
B) $g ( x ) = \frac { 1 } { ( x - 3 ) ^ { 2 } }$
C) $h ( x ) = ( 2 x - 1 ) ^ { 2 }$
D) $F ( x ) = \frac { 3 } { x } - 6$
E) $G ( x ) = | x |$

Question

Which of the following functions is one-to-one?

A) $f ( x ) = \lfloor x \rfloor + 2$
B) $g ( x ) = \frac { 1 } { ( x - 3 ) ^ { 2 } }$
C) $h ( x ) = ( 2 x - 1 ) ^ { 2 }$
D) $F ( x ) = \frac { 3 } { x } - 6$
E) $G ( x ) = | x |$

Quizplus · Accepted Answer

Function D, $F(x) = \frac{3}{x} - 6$, is one-to-one because for every x value, there is a unique y value, and it passes the horizontal line test. The other functions are not one-to-one because they either repeat y values for different x values or are not injective.

Which of the Following Functions Is One-To-One? A) f(x)=⌊x⌋+2f ( x ) = \lfloor x \rfloor + 2f(x)=⌊x⌋+2

Which of the Following Functions Is One-To-One?

A) $f ( x ) = \lfloor x \rfloor + 2$