Find space inverse space of space straight f left parenthesis straight x right parenthesis equals space straight a to the power of straight x minus straight a to the power of negative straight x end exponent divided by straight a to the power of straight x plus straight a to the power of negative straight x end exponent

Asked by Moorti | 5th Jul, 2019, 06:15: PM

Expert Answer:

f(x) = y = ax - a-x / ax + a-x
begin mathsize 16px style straight y equals fraction numerator straight a to the power of straight x minus straight a to the power of negative straight x end exponent over denominator straight a to the power of straight x plus straight a to the power of negative straight x end exponent end fraction
straight y equals fraction numerator straight a to the power of 2 straight x end exponent minus 1 over denominator straight a to the power of 2 straight x end exponent plus 1 end fraction
ya to the power of 2 straight x end exponent plus straight y equals straight a to the power of 2 straight x end exponent minus 1
straight y plus 1 equals straight a to the power of 2 straight x end exponent minus ya to the power of 2 straight x end exponent
straight y plus 1 equals straight a to the power of 2 straight x end exponent left parenthesis 1 minus straight y right parenthesis
straight a to the power of 2 straight x end exponent equals fraction numerator straight y plus 1 over denominator 1 minus straight y end fraction
loga to the power of 2 straight x end exponent equals log open parentheses fraction numerator straight y plus 1 over denominator 1 minus straight y end fraction close parentheses
2 xloga equals log open parentheses fraction numerator straight y plus 1 over denominator 1 minus straight y end fraction close parentheses
straight x equals fraction numerator 1 over denominator 2 loga end fraction log open parentheses fraction numerator straight y plus 1 over denominator 1 minus straight y end fraction close parentheses
straight x equals 1 over loga squared log open parentheses fraction numerator straight y plus 1 over denominator 1 minus straight y end fraction close parentheses end style

Answered by Sneha shidid | 8th Jul, 2019, 11:17: AM