Question

state whether the function f(x)= e^x+e^-x/2 is even or odd. please help me to solve this question . ​

Answer 1

SOLUTION

TO CHECK

Even / odd function for the below function

$\displaystyle \sf{f(x) = \frac{ {e}^{x} + {e}^{ - x} }{2} }$

CONCEPT TO BE IMPLEMENTED

A function f(x) is said to be

1. Even function if f( - x ) = f(x)

2. Odd function if f( - x ) = - f(x)

EVALUATION

Here the given function is

$\displaystyle \sf{f(x) = \frac{ {e}^{x} + {e}^{ - x} }{2} }$

Now

$\displaystyle \sf{f( - x) = \frac{ {e}^{ - x} + {e}^{ - ( - x)} }{2} }$

$\displaystyle \sf{ \implies \: f( - x) = \frac{ {e}^{ - x} + {e}^{ x} }{2} }$

$\displaystyle \sf{ \implies \: f( - x) = \frac{ {e}^{x} + {e}^{ - x} }{2} }$

$\displaystyle \sf{ \implies \: f( - x) = f(x)}$

Hence $\displaystyle \sf{f(x) = \frac{ {e}^{x} + {e}^{ - x} }{2} }$ is an even function

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Answer 2

Answer:

The function is Even Function