Question

in a meeting a government officer wants to distribute certain numbers of apples equally among the physically handicapped children . if the number of children was 2 less, then each of them would have got one apple more. Again when the ten officers present in the day included , then each of them will get 3 apple less .find the number of the handicapped children and the number of apples

Answer 1

f(x)= \cfrac{3}{x^2}+2 f(x)=

x

2

3

+2 .

Given that x is in the denominator, it cannot be equal to 0.

So, the domain of this function is x \in (- \infty, 0)∪(0; + \infty)x∈(−∞,0)∪(0;+∞).

The value \cfrac{3}{x^2}

x

2

3

could not be less than 0 because x^2 \gt 0 x

2

>0 for all x.

The value \cfrac{3}{x^2}

x

2

3

could not be equal 0.

All of theese means that value \cfrac{3}{x^2}+2 \gt 2

x

2

3

+2>2 for all x.

So, the range of f(x)f(x) is (2, + \infin )(2,+∞) .

Answer: Domain is (- \infty, 0)∪(0, + \infty)(−∞,0)∪(0,+∞) , range is (2, + \infin )(2,+∞) .