Solution to ) Determine whether each of these functions is a bijection from R to R. (i) … - Sikademy
Author Image

Archangel Macsika

) Determine whether each of these functions is a bijection from R to R. (i) f(x) = -3x + 4 (ii) f(x) = 2x + 1 (iii) f(x) = x 2 + 1 (iv) f(x) = -3x 2 + 7 (v) f(x) = (x+1) (x+2)

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

Get the Answers Now!

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

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

(ii) \forall x \in R\; \; \exist !y = 2x+1 and \forall y \in R \; \exist!x= \frac{y-1}{2} \Rightarrow bijection

(iii) y = x^2+1y(-1) = y(1) = 2 \Rightarrow is not injective, thus not bijection

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

(v) y = (x+1)(x+2)= x^2+2x+2 = (x+1)^2+1y(-3) = y(1) = 5 \Rightarrow is not injective, thus not bijection


Related Answers

Was this answer helpful?

Join our Community to stay in the know

Get updates for similar and other helpful Answers

Question ID: mtid-5-stid-8-sqid-3766-qpid-2465