Find the range of function f(x)=2/(|3-|x-1|-5x|-9)?

Asked by Jyoti Chandra Azad | 21st May, 2014, 09:32: AM

Expert Answer:

Please have a look at the graph ...its range is from - infinity to + infinity except '0', and has local maxima at x = 1/2 , whose value is - 2/9 (it will lie on the green line).
f open parentheses x close parentheses equals fraction numerator 2 over denominator open parentheses open vertical bar 3 space minus space open vertical bar space x space minus space 1 close vertical bar space minus space 5 x space close vertical bar space minus space 9 close parentheses end fraction F o r space x space minus space 1 space greater than space 0 f open parentheses x close parentheses equals fraction numerator 2 over denominator open parentheses open vertical bar 3 space plus space x minus space 1 minus space 5 x close vertical bar space minus space 9 close parentheses end fraction space space space space space space space equals space fraction numerator 2 over denominator open parentheses open vertical bar 2 space minus space 4 x close vertical bar minus 9 close parentheses end fraction N o w comma 2 space minus space 4 x space greater or equal than 0 space rightwards double arrow x space greater or equal than 1 half f open parentheses x close parentheses equals fraction numerator 2 over denominator open parentheses 2 space minus space 4 x space minus space 9 close parentheses end fraction space space space space space space space equals space fraction numerator 2 over denominator minus 7 minus 4 x end fraction F o r space x space equals space 1 half f open parentheses x close parentheses equals fraction numerator 2 over denominator minus 7 minus 4 cross times begin display style 1 half end style end fraction equals fraction numerator 2 over denominator minus 9 end fraction equals minus 2 over 9

Answered by Avinash Soni | 21st May, 2014, 11:10: AM

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