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How do you find the domain and range of #h(x) = e^(-x^2)#?

Answer 1

Abigail Allen

The domain is the set of all real number hence #D_f=(-oo,+oo)#

The range is #R_f=(0,1] #

Because #e^(x^2)>=x^2+1# hence #1/e^(x^2)<=1/(x^2+1)<=1#

but always #1/e^(x^2)>0#

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Answer 2

Savannah Anderson

To find the domain of h(x), consider the values of x for which the function is defined. Since the exponential function is defined for all real numbers, the domain of h(x) is (-∞, ∞). To find the range, observe that as x approaches infinity, e^(-x^2) approaches 0. Therefore, the range of h(x) is (0, ∞).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.