Question

find range of f(x)=x2+2 and xbelongs to R​

Answer 1

Answer:

Range R ={2,3,6,11,18,......}

Step-by-step explanation:

$given \: \: f(x) = x {}^{2} + 2 \: \: where \: x \: belongs \: to \: real \: number.$

$real \: numbers \: can \: be \: positive \: or \: negative.$

$therefore \: \: f( - 3) = 9 + 2 = 11 \\ \: \: \: f( - 2) = 4 + 2 = 6 \\ \: \: \: f( - 1) = 1 + 2 = 3 \\ \: \: \: f(0) = 0 + 2 = 2 \\ \: \: \: f(1) = 1 + 2 = 3 \\ \: \: \: f(2) = 4 + 2 = 6 \\ \: \: \: f(3) = 9 + 2 = 11$

By continuing this way we get all positive integers,.

Note that the elements of the range cannot be repeated.

Therefore, Range R = { 2,3,6,11,18,......}

Note that the numbers between each element is the increasing order of the even numbers

That is the numbers between 2 and 3 is 0,the numbers between 3 and 6 is 2 and it goes on.