A function $f:A \rightarrow B$, where $A = \{ x: - 1 \leq x \leq 1\}$ and $B = \{ y:1 \leq y \leq 2\}$, is defined by the rule $y = f(x) = 1 + x^{2}$. Which of the following statement is true?

Question

Dr. Abubacker · Accepted Answer

(b)
Since, $A = \{ x: - 1 \leq x \leq 1\}$
And $B = \left\{ y:1 \leq y \leq 2 ight\}$
Also, $\ y = f(x) = 1 + x^{2}$
For $\ \ \ \ x = - 1,\ y = 1 + ( - 1)^{2} = 2$
And for $x = 1,\ y = 1 + 1^{2} = 2$
$	herefore f$ is not injective. (one-one)
Here, $\forall B$ their is a preimage.
Hence, $f$ is surjective.

Q. A function $f:A \rightarrow B$, where $A = \{ x: - 1 \leq x \leq 1\}$ and $B = \{ y:1 \leq y \leq 2\}$, is defined by the rule $y = f(x) = 1 + x^{2}$. Which of the following statement is true?

Explanation

Reviewed by Dr. Abubacker

Want more practice?