Question

lf $f\left(x\right)=\cosh x+\sinh x$ then $f(x_1+x_2+\dots \dots \dots \dots .+x_n)=$

• A. $1$
• B. $f(x_1+x_2+\dots \dots \dots \dots .+x_n)$
• C. $0$
• D. $f\left(x_1\right).f\left(x_2\right)\dots ..f\left(x_n\right)$

Answer 1

The correct option is D $f\left(x_1\right).f\left(x_2\right)\dots ..f\left(x_n\right)$

$f\left(x\right)=\sinh x+\cosh x$

Now

$\sinh x=\frac{e^x-e^{-x}}{2}$

And

$\cosh x=\frac{e^x+e^{-x}}{2}$

Hence

$f\left(x\right)=\sinh x+\cosh x$

$=\frac{e^x-e^{-x}}{2}+\frac{e^x+e^{-x}}{2}$

$=e^x$

Hence

$f\left(x\right)=e^x$

Now

$f(x_1+x_2+x_3+x_4+...x_n)$

$=e^{x_1+x_2+x_3+...x_n}$

$=e^{x_1}.e^{x_2}.e^{x_3}...e^{x_n}$

$=f\left(x_1\right)f\left(x_2\right)f\left(x_3\right)...f\left(x_n\right)$