Discrete Math Determine whether each of the following functi

Discrete Math.

Determine whether each of the following functions is a bijection from R to R: f(x) = -3x + 4 f(x) = -3x^2 + 7

Solution

1)
The function is a bijection. The value of f(x) will be distinct for different values of x. Let us try to find the inverse:

y = -3x+4
(4-y)/3 = x

so f\'(x) = (4-x)/3

2)
The function is not bijection. The value of -3x^2+7 is same for k and -k for any k that belongs to R. Therefore the function is not a bijection.