Which of the following functions f : {0, 1, 2, 3} {0, 1, ..., 7} are one-to-one?

Question

Which of the following functions f : {0, 1, 2, 3} {0, 1, ..., 7} are one-to-one? a. f(x) = x2 mod 8 b. f(x)=x3 mod8 c. f(x)=(x3 –x)mod8 d. f(x)=(x3 –2x)mod8 e. f(0)=3,f(1)=1,f(2)=4,f(3)=1
Which of the following functions f : {0, 1, 2, 3} {0, 1, ..., 7} are one-to-one? a. f(x) = x2 mod 8 b. f(x)=x3 mod8 c. f(x)=(x3 –x)mod8 d. f(x)=(x3 –2x)mod8 e. f(0)=3,f(1)=1,f(2)=4,f(3)=1
Which of the following functions f : {0, 1, 2, 3} {0, 1, ..., 7} are one-to-one? a. f(x) = x2 mod 8 b. f(x)=x3 mod8 c. f(x)=(x3 –x)mod8 d. f(x)=(x3 –2x)mod8 e. f(0)=3,f(1)=1,f(2)=4,f(3)=1

Explanation / Answer

(a). f(x) = x^2 mod 8

=> f(0) = 0, f(1) = 1, f(2) = 4, f(3) = 1

So this not one-one as both f(1) and f(3) is 1

(b). f(x) = x^3 mod 8

=> f(0) = 0, f(1) = 1, f(2) = 0, f(3) = 3

So this not one-one as both f(0) and f(2) is 0

(c). f(x) = (x^3-x) mod 8

=> f(0) = 0, f(1) = 0, f(2) = 6, f(3) = 0

So this not one-one as f(0), f(1) and f(3) is 0

(d). f(x) = (x^3-2x) mod 8

=> f(0) = 0, f(1) = 7, f(2) = 4, f(3) = 5

So this one-one as all the function values are different.

(e) not one-one as f(1) = f(3) = 1

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