Answer to Question #125402 in Algebra for EMMANUEL

Question #125402

Find the domains of f(x)= (4-x2)1/2 and h(x)= (3-x)1/2.


1
Expert's answer
2020-07-07T17:21:54-0400

Given "f(x)=\\sqrt{4-x^2}" ,"h(x)=\\sqrt{3-x},"

"f(x)" is defined if "4-x^2\\geq 0\\implies(2-x)(2+x)\\geq0" . Thus, "x\\in[-2,2]" ,hence the domain of "f" is "D_f=[-2,2]" .

Now, "h(x)" is defined if "3-x\\geq0\\implies x\\in(-\\infty,3]" ,hence the domain of "h" is "D_h=(-\\infty,3]" .


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