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G(x)=1/2x^2+5 Domain:Range:Help please

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The domain of a function is the interval containing all the values for which the function is well defined. Since this is not a rational function, i.e., it's not a fraction of polynomials, the function is well defined for all values of x. Therefore, the domain is:

Domain: (-∞, ∞)

Now, in order to find the range, we need to notice that is always positive or zero. Therefore, we have:

x² ≥ 0

(1/2)x² ≥ 0

(1/2)x² + 5 ≥ 0 + 5

(1/2)x² + 5 ≥ 5

g(x) ≥ 5

Thus, the range of the function is all the values greater than or equal to 5:

Range: [5, ∞)

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