Let  f:A to A be defined as f(x)=2^(x(x+1))  where,
A={x€R:x>=1}
Find inverse of the function ?????

Asked by vaish.agrawal | 18th Jun, 2015, 12:41: PM

Expert Answer:

y equals 2 to the power of x open parentheses x plus 1 close parentheses end exponent rightwards double arrow x open parentheses x plus 1 close parentheses equals log subscript 2 open parentheses y close parentheses rightwards double arrow x squared plus x minus log subscript 2 open parentheses y close parentheses equals 0 rightwards double arrow x equals fraction numerator negative 1 plus-or-minus square root of 1 plus 4 log subscript 2 open parentheses y close parentheses end root over denominator 2 end fraction T a k i n g space p l u s space s i g n space left parenthesis sin c e space x greater or equal than 1 right parenthesis comma space w e space g e t x equals fraction numerator negative 1 plus square root of 1 plus 4 log subscript 2 open parentheses y close parentheses end root over denominator 2 end fraction rightwards double arrow f to the power of negative 1 end exponent open parentheses y close parentheses equals fraction numerator negative 1 plus square root of 1 plus 4 log subscript 2 open parentheses y close parentheses end root over denominator 2 end fraction rightwards double arrow f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative 1 plus square root of 1 plus 4 log subscript 2 open parentheses x close parentheses end root over denominator 2 end fraction

Answered by satyajit samal | 19th Jun, 2015, 11:52: PM