Match each of the following inverse hyperbolic functions to

Match each of the following inverse hyperbolic functions to its log form or it\'s value. cosh^-1 (x) sinh^-1 (x) tanh^-1 (x) cosh^-1 (13/12) sinh^-1 (4/3) tanh^-1 (-20/9) A. ln(3/7) B. 1/2 ln(1 + x/1 - x) C. ln[x + squareroot x^2 - 1) D. ln(3) E. ln(3/2) F. ln(x + squareroot x^2 + 1)

Solution

(1) arccosh(x) =   (C) ln(x+sqrt(x^2-1))

(2) arcsinh(x) =   (F) ln(x+sqrt(x^2+1))

(3) arctanh(x) = (B) (1/2)(ln((1+x)/(1-x))

(4) arccosh(13/12)= (E) ln(3/2)

(5) arcsinh(4/3) = (D) ln(3)

(6) arctanh(-20/9)= (A) ln(3/7)