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Question: If \(f(x) = \cosh x - \sinh x,\) then \(f(x_{1} + x_{2} + ... + x_{n})\) is equal to....

If f(x)=cosh⁡x−sinh⁡x,f(x) = \cosh x - \sinh x, then f(x1+x2+...+xn)f(x_{1} + x_{2} + ... + x_{n}) is equal to.

A

f(x1).f(x2)........f(xn)f(x_{1}).f(x_{2})........f(x_{n})

B

f(x1)+f(x2)+......+f(xn)f(x_{1}) + f(x_{2}) + ...... + f(x_{n})

C

0

D

1

Answer

f(x1).f(x2)........f(xn)f(x_{1}).f(x_{2})........f(x_{n})

Explanation

Solution

f(x)=e−xf(x) = e^{- x}

⇒ f(x1+x2+.....+xn)=e−(x1+x2+....+xn)f(x_{1} + x_{2} + ..... + x_{n}) = e^{- (x_{1} + x_{2} + .... + x_{n})}

=e−x1.e−x2....e−xn=f(x1).f(x2)...f(xn)= e^{- x_{1}}.e^{- x_{2}}....e^{- x_{n}} = f(x_{1}).f(x_{2})...f(x_{n}).