The function begin mathsize 12px style f open parentheses x close parentheses equals log open parentheses x plus square root of x squared plus 1 end root close parentheses end style,is
i.neither an even nor an odd function
ii.an even function
iii.an odd function
iv.a periodic function

Asked by sunil2791 | 11th Jun, 2017, 11:35: AM

Expert Answer:

begin mathsize 16px style straight f left parenthesis straight x right parenthesis equals log left parenthesis straight x plus square root of straight x squared plus 1 end root right parenthesis
rightwards double arrow straight f left parenthesis negative straight x right parenthesis equals log left parenthesis negative straight x plus square root of straight x squared plus 1 end root right parenthesis
straight f left parenthesis straight x right parenthesis plus straight f left parenthesis negative straight x right parenthesis equals log left parenthesis straight x plus square root of straight x squared plus 1 end root right parenthesis plus log left parenthesis negative straight x plus square root of straight x squared plus 1 end root right parenthesis
straight f left parenthesis straight x right parenthesis plus straight f left parenthesis negative straight x right parenthesis equals log open square brackets open parentheses straight x plus square root of straight x squared plus 1 end root close parentheses open parentheses negative straight x plus square root of straight x squared plus 1 end root close parentheses close square brackets
straight f left parenthesis straight x right parenthesis plus straight f left parenthesis negative straight x right parenthesis equals log open parentheses straight x squared plus 1 minus straight x squared close parentheses
straight f left parenthesis straight x right parenthesis plus straight f left parenthesis negative straight x right parenthesis equals 0
straight f left parenthesis negative straight x right parenthesis equals negative straight f left parenthesis straight x right parenthesis
Hence space straight f left parenthesis straight x right parenthesis space is space odd space function. end style

Answered by Sneha shidid | 12th Jun, 2017, 08:40: AM