Write the equivalent definition and draw the graphs of the following functions. `f(x)=sgn((log)_e|x|)`

Answer

(a) `f(x)={(1",",|x| gt 1),(0",",|x|=1),(-1",",0 lt |x| lt 1):}`
(b) `f(x)={(-1",",x lt -1","0lt x lt 1),(1",",-1 lt x lt 0","x gt 1),(0",", x= -1","0","1):}`

Explanation

(a)

From the graph`f(x)={(1",",|x| gt 1),(-1",",0 lt |x| lt 1),(0",",|x|=1):}`
(b)

From the graph, `f(x)={(-1",",x lt -1","0lt x lt 1),(1",",-1 lt x lt 0","x gt 1),(0",", x= -1","0","1):}`.