For each equation below, determine if the function is Odd, Even, or Neither
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Mar 28,2025

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For each equation below, determine if the function is Odd, Even, or Neither
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Ask by Horton Newton. in the United States

Mar 28,2025

UpStudy AI · Accepted Answer

**Step 1. Function $$ f(x) = \frac{2}{x} $$**

- Compute $$ f(-x) $$:
  $$
  f(-x) = \frac{2}{-x} = -\frac{2}{x} = -f(x)
  $$
- Since $$ f(-x) = -f(x) $$, the function is **Odd**.

---

**Step 2. Function $$ g(x) = \sqrt{x} $$**

- The domain of $$ g(x) $$ is $$ x \ge 0 $$.
- For an even or odd function test, both $$ f(x) $$ and $$ f(-x) $$ need to be in the domain.
- Since $$ g(-x) = \sqrt{-x} $$ is not real when $$ x > 0 $$, the symmetry conditions cannot be applied properly.
- Therefore, the function is **Neither**.

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**Step 3. Function $$ h(x) = 2 x^4 $$**

- Compute $$ h(-x) $$:
  $$
  h(-x) = 2 (-x)^4 = 2 x^4 = h(x)
  $$
- Since $$ h(-x) = h(x) $$, the function is **Even**.

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**Final Answers:**

- $$ f(x)=\frac{2}{x} $$ is **Odd**.
- $$ g(x)=\sqrt{x} $$ is **Neither**.
- $$ h(x)=2x^4 $$ is **Even**.
- $$ f(x)=\frac{2}{x} $$ is **Odd**. - $$ g(x)=\sqrt{x} $$ is **Neither**. - $$ h(x)=2x^4 $$ is **Even**.

For each equation below, determine if the function is Odd, Even, or Neither
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For each equation below, determine if the function is Odd, Even, or Neither Select an answer Select an answer Select an answer Submit Question

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For each equation below, determine if the function is Odd, Even, or Neither
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