Let f(x)=x/3xsquared+1 and g(x)=square root of 1-x
Find
1. f+g
2. F-g
3. F/g
4. F of g
5. G of f
6. State the domain of g of f
1
Expert's answer
2021-05-18T05:48:02-0400
Given,f(x)=3x2+1xandg(x)=1−x.1.f+g=3x2+1x+1−x=3x2+1x+1−x2.f−g=3x2+1x−1−x=3x2+1x−1−x3.gf=1−x3x2+1x=(3x2+1)1−xx4.fοg=f(g(x))=f(1−x)=3(1−x)2+11−x=3(1−x)2+11−x=3(1−2x+x2)+11−x=3x2−6x+41−x5.gοf=g(f(x))=g(3x2+1x)=1−3x2+1x=3x2+13x2+1−x=3x2+13x2−x+16.Domain of square root function is Positive real numbers.Therefore, denominator>0.3x2+1<0Since, 3x2+1is always positive.Therefore,domain of gοf=3x2+13x2−x+1 is real numberi.e.,x∈R.
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