Question

How do you determine if \[f(x) = 7\] is an even or odd function?

Answer 1

Hint: We use the definition of even and odd functions and substitute the values of x to check if the value of function changes when we change the value of x.

Complete step-by-step answer:
We have to check that the given function \[f(x) = 7\] is an even or an odd function.
We will define even and odd functions first and then check the given function.
Even function: A function ‘f’ is said to be an even function if and only if \[f( - x) = f(x)\] for all ‘x’ in the domain of the function ‘f’.
Odd function: A function ‘f’ is said to be an odd function if and only if \[f( - x) = - f(x)\] for all ‘x’ in the domain of the function ‘f’.
We are given the function \[f(x) = 7\]
Now we substitute the value of x as 7 and check the value of the function
\[ \Rightarrow f(7) = 7\] … (1)
Similarly, we substitute the value of x as -7 and check the value of the function
\[ \Rightarrow f( - 7) = 7\] … (2)
We can see that the value of the function remains the same i.e. 7 whatever be the value of x.
Also, the value of the function comes out to be always positive, so the function must be an even function.

\[\therefore \] \[f(x) = 7\] is an even function.

Note:
Many students get confused while choosing the function to be an odd or an even function as the given function is a constant function as the value of the function remains the same whatever be the value of x. Keep in mind constant function is always an even function whatever be the value of constant, negative or positive.