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  • Let f : R → R be defined by f(x) = 3x2 – 5 and g : R → R by g(x) = x/(x2+1), then gof is (a) (3x2-5)/(9x4-30x2+ 26)

Let f : R \rightarrow R  be defined by f(x) = 3x\textsuperscript{2} - 5  and g : R \rightarrow R  by g(x) = x/(x\textsuperscript{2}+1), then gof is 

\\(a) (3x\textsuperscript{2}-5)/(9x\textsuperscript{4}-30x\textsuperscript{2}+ 26)\\ (b) (3x\textsuperscript{2}-5)/(9x\textsuperscript{4}-6x\textsuperscript{2}+ 26) \\(c) 3x\textsuperscript{2}/(x\textsuperscript{4}+2x\textsuperscript{2}-4) \\(d) (3x\textsuperscript{2})/(9x\textsuperscript{4}-30\textsuperscript{2}+2)\\

Answers (1)

(a) 

Given, f(x) = 3x\textsuperscript{2} - 5 \ and \ g(x) = x/(x\textsuperscript{2}+1)\\

Therefore,

\\gof = gof (x) = g(3x\textsuperscript{2}-5) = (3x\textsuperscript{2}-5)/[(3x\textsuperscript{2}-5)\textsuperscript{2}+1]\\ = (3x\textsuperscript{2}-5)/(9x\textsuperscript{4}-30x\textsuperscript{2}+ 26)\\

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