Question
3. Determine whether the function f(x)=2times 5=3times 3=7 is even, odd, or neither. Explain your reasoning.
Solution
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QuintinMaster · Tutor for 5 years
Answer
### Even
Explain
## Step 1: Evaluate the function<br /><br />### The given function $f(x) = 2 \times 5 = 3 \times 3 = 7$ simplifies to $f(x) = 7$. This means the function is a constant function, always equal to 7, regardless of the input value of $x$.<br /><br />## Step 2: Test for even function<br /><br />### A function is even if $f(-x) = f(x)$ for all $x$ in the domain. Since $f(x) = 7$ for all $x$, $f(-x)$ will also be 7. Thus, $f(-x) = f(x) = 7$.<br /><br />## Step 3: Test for odd function<br /><br />### A function is odd if $f(-x) = -f(x)$ for all $x$ in the domain. In our case, $f(-x) = 7$, and $-f(x) = -7$. Since $7 \neq -7$, the function is not odd.<br /><br />## Step 4: Conclusion<br /><br />### Since $f(-x) = f(x)$, 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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