Question

Which of the following mapped diagram satisfies given function defined from $X$ to $Y$.
$y=2x^2-2x+2$
$X:\{\frac{3}{2},\sqrt{2},-1,1,0\}$
$Y:\{2,6,\frac{7}{2},6-2\sqrt{2}\}$
Given that $x\in \text{X}\&y\in \text{Y}$

• A.
• B.
• C.

Answer 1

The correct option is A

Given that function is defined from set $X$ to set $Y$
Given rule is $y=2x^2-2x+2$
$X:\{\frac{3}{2},\sqrt{2},-1,1,0\}$
$Y:\{2,6,\frac{7}{2},6-2\sqrt{2}\}$
Given that $x\in \text{X}\&y\in \text{Y}$

Here, we need put each value of set $X$ in given rule to find value of $y$.
Value of $x$ are input here and value of $y$ are output.

Collection of given input values is Domain and collection of output values is Range.

On putting each value of $x$, mapped diagram will be:

$x=\frac{3}{2}\Rightarrow 2\times (\frac{3}{2}{)}^2-2\times (\frac{3}{2})+2=\frac{7}{2}x=\sqrt{2}=2(\sqrt{2}{)}^2-2\sqrt{2}+2=6-2\sqrt{2}x=-1\Rightarrow 2(-1{)}^2-2(-1)+2=6x=1\Rightarrow 2(1{)}^2-2\left(1\right)+2=2x=0\Rightarrow 2(0{)}^2-2(0)+2=2$