Question

Determine algebraically if f(x)=√1-x is a function even, odd, or neither.

Answer 1

we have the function

`f(x)=\sqrt[]{1-x}`

step 1

Verify if the function is even

Remember that

If a function satisfies f(−x) = f(x) for all x it is said to be an even function

so

`\begin{gathered} f(-x)=\sqrt[]{1-(-x)} \\ f(-x)=\sqrt[]{1+x} \end{gathered}`

therefore

f(x) is not equal to f(-x)

the function is not even

step 2

Verify if the function is odd

Remember that

A function is odd if −f(x) = f(−x), for all x

`\begin{gathered} -f(x)=-\sqrt[]{1-x} \\ f(-x)=\sqrt[]{1+x} \end{gathered}`

therefore

-f(x) is not equal to f(-x)

The function is not odd

therefore

the answer is neither