Find the domain and the range of the real function, `f(x)=(1)/(sqrt(x+ – InterviewSolution

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1.	Find the domain and the range of the real function, `f(x)=(1)/(sqrt(x+\|x\|))`.
Answer» We have, `f(x)=(1)/(sqrt(x+\|x\|))` Now, `\|x\|={{:(x",when "xge0),(-x",when "xlt0):}` `impliesx+\|x\|={{:(x+x",when "xge0),(x-x",when "xlt0):}` `impliesx+\|x\|={{:(2x",when "xge0),(0",when "xlt0):}` `impliesx+\|x\|gt0,"when "xgt0` `impliesf(x)=(1)/(sqrt(x+\|x\|))` assumes real values only when `x+\|x\|gt0` and this happens only when `xgt0`. `:."dom "(f)=(0,oo)`.

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