Show that `f(x)=(1)/sqrt(x-|x|)` is not defined for any `x""inR`. How – InterviewSolution

InterviewSolution

1.	Show that `f(x)=(1)/sqrt(x-\|x\|)` is not defined for any `x""inR`. How will you define dom (f) and range (f)?
Answer» We have, `f(x)=(1)/sqrt(x-\|x\|)` Now, `implies\|x\|={{:(x",when "xge0),(-x",when "xlt0):}` `impliesx-\|x\|={{:(x-x",when "xge0),(x+x",when "xlt0):}` `impliesx-\|x\|={{:(0",when "xge0),(2x",when "xlt0):}` `implies(1)/(sqrt(x-\|x\|))` is not defined for any `x""inR`. `:."dom "(f)=phi" and range "(f)=phi`.

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