Question

Range and domain of x/(2+x^2)

Answer 1

Answer:

The domain of a function is the set of all real values of x that will give real values for y. Therange of a function is the set of all real values of ythat you can get by plugging real numbers into x. The quadratic parent function is y = x2. The graph of this function is shown below.

Answer 2

Answer:

first of all for finding the domain

we have to look first at the denominator

$x \div (2 + x ^{2} )$

here we have 2+x² in the denominator hence due to squaring of x either x is positive or negative real no the value will remain positive and not 0 (which is required)

therefore the x can be any real no

hence domain= {R}

now as we have discussed above that domain remains positive but it is not comoulsory that the numirator will be +ve so

(because if we put x as -ve real no then the whole value become -ve )

therefore here the range can be set of all real nos because it can vary from

$- \infty \: to \: + \infty$

hence by this we get that

$range = ( - \infty \: to \: \infty )$

hope it helped

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