Question

Determine Which of these function are bijection from the set of real number to itself

1- f(x)=-3x+4

2- f(x)=-3x2+7

3- f(x)=(x+1)/(x+2)

Answer 1

1) $\forall x \in R\; \; \exist !y = -3x+4$ and $\forall y \in R \; \exist!x= \frac{4-y}{3} \Rightarrow$ bijection

2) $y=-3x^2+7$ , $y(-1) = y(1) = 4 \Rightarrow$ is not injective, thus not bijection

3) f(x)=(x+1)/(x+2). It is not a function from R to R because it is not defined at −2! So $f$ certainly cannot be a bijective function.