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Asked Oct 25, 2019
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Q 9. (a) Find the inverse function of cosh(x). (Hint set z = e and invert that. Then replace
e for z).
(b) Find the derivative of cosh1 (x) using implicit differentiation and by differentiating the
function you found in item (a).
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Q 9. (a) Find the inverse function of cosh(x). (Hint set z = e and invert that. Then replace e for z). (b) Find the derivative of cosh1 (x) using implicit differentiation and by differentiating the function you found in item (a).

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Expert Answer

Step 1

(a)Find the inverse function of cosh(x)

f(x) coshx
e e
x
2
Let f(x)y
Then f(y)x
e e
= x
2
1
e 2x
e
e2y-2xe1= 0
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f(x) coshx e e x 2 Let f(x)y Then f(y)x e e = x 2 1 e 2x e e2y-2xe1= 0

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Step 2

Solve the equ...

2xt4x2-4
2
= xt-
y= In{x+vx -1
Here, y is defined when x2-120
x 21 or x1
If x-1 then x-
/x2-10
Replace y by f(x)
Thus, the inverse function is f(x)= In(xt Vx* -1
help_outline

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2xt4x2-4 2 = xt- y= In{x+vx -1 Here, y is defined when x2-120 x 21 or x1 If x-1 then x- /x2-10 Replace y by f(x) Thus, the inverse function is f(x)= In(xt Vx* -1

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