3. Determine whether the function f(x)=2times 5=3times 3=7 is even, odd, or neither. Explain your reasoning.

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Answer 1

## Step 1: Evaluate the function### The given function

simplifies to

. This means the function is a constant function, always equal to 7, regardless of the input value of

.## Step 2: Test for even function### A function is even if

for all

in the domain. Since

for all

,

will also be 7. Thus,

.## Step 3: Test for odd function### A function is odd if

for all

in the domain. In our case,

, and

. Since

, the function is not odd.## Step 4: Conclusion### Since

, the function is even. Because it satisfies the condition for an even function and not the condition for an odd function, it is not neither.

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