What is the domain and range of $y = \frac{1}{2} x^{2} + 4$ $y=1/2x^2+4$ ?

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What is the domain and range of $y = \frac{1}{2} x^{2} + 4$ $y=1/2x^2+4$ ?

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Answer 1 · 2014-10-21T19:25:54

Consider the function $y = f (x)$ $y= f(x)$

The domain of this function is all the values of x for which the function holds. The range is all those values of y for which the function is valid.

Now, coming to your question.
$y = \frac{x^{2}}{2} + 4$ $y = x^2 / 2 + 4$
This function is valid for any real value of x. Thus the domain of this function is the set of all real numbers, i.e. , $R$ $R$ .

Now, separate out x.
$y = \frac{x^{2}}{2} + 4$ $y= x^2 /2 +4$

=> $y - 4 = \frac{x^{2}}{2}$ $y-4 = x^2 /2$

=> $2 (y - 4) = x^{2}$ $2(y-4) = x^2$

=> ${2 (y - 4)}^{\frac{1}{2}} = x$ ${2(y-4)}^(1/2) = x$

Thus, the function is valid for all real numbers greater than or equal to 4. Therefore the range of this function is [4, $\infty$ $oo$ ).

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What is the domain and range of $y = \frac{1}{2} x^{2} + 4$ $y=1/2x^2+4$ ?

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