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arccos((x-1)(x-5))/(X(x-2)(x-3))
Find its range

Asked by sudheerkapoor67 8th November 2017, 5:41 AM
Answered by Expert
Answer:
straight y equals cos to the power of negative 1 end exponent open parentheses fraction numerator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 5 right parenthesis over denominator straight x left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction close parentheses
the space range space of space straight y equals cos to the power of negative 1 end exponent open parentheses x close parentheses space is space left square bracket 0 comma straight pi right square bracket
the space domain space will space be
minus 1 less or equal than fraction numerator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 5 right parenthesis over denominator straight x left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction less or equal than 1
that space is space
minus 1 less or equal than fraction numerator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 5 right parenthesis over denominator straight x left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction space and space fraction numerator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 5 right parenthesis over denominator straight x left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction less or equal than 1
solve space seperately space and space take space their space intersection
Also space exclude space values space of space straight x equals 0 comma straight x equals 2 comma straight x equals 3 space from space the space domain space since space denominator
of space fraction numerator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 5 right parenthesis over denominator straight x left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction space becomes space zero. space
Answered by Expert 11th December 2017, 12:59 PM
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