(ix) It is possible to extract a metal from its oxide it the free energy of formation of the oxide of the reducing agent is lower than that of the oxidising agent.

Explanation

To determine whether the statement is true or false, we need to analyze the conditions under which a metal can be extracted from its oxide using a reducing agent.

### Step-by-Step Solution:

1. **Understanding the Statement**: The statement claims that a metal can be extracted from its oxide if the free energy of formation of the oxide of the reducing agent is lower than that of the oxidizing agent.

2. **Defining the Reducing and Oxidizing Agents**:
- Let’s denote the reducing agent as \( M \) and its oxide as \( MO_2 \).
- Let’s denote the oxidizing agent as \( K \) and its oxide as \( KO_2 \).

3. **Free Energy of Formation**:
- The free energy of formation for the oxide of the reducing agent is represented as \( \Delta G_1 \) for \( MO_2 \).
- The free energy of formation for the oxide of the oxidizing agent is represented as \( \Delta G_2 \) for \( KO_2 \).

4. **Feasibility of the Reaction**:
- For \( M \) to reduce \( KO_2 \) (the oxidizing agent), the reaction must be spontaneous. This is determined by the Gibbs free energy change.
- The reaction is spontaneous if the change in Gibbs free energy (\( \Delta G \)) is negative.

5. **Condition for Spontaneity**:
- The condition for \( M \) to act as a reducing agent and \( K \) to act as an oxidizing agent is that the free energy of formation of the oxide of the reducing agent must be more negative than that of the oxidizing agent:
\[ \Delta G_1 < \Delta G_2 \]
- This implies that \( | \Delta G_1 | > | \Delta G_2 | \) (the absolute value of \( \Delta G_1 \) should be greater than that of \( \Delta G_2 \)).

6. **Conclusion**:
- Since the original statement claims the opposite (that \( \Delta G_1 \) should be lower), the statement is **false**.

### Final Answer:
The statement is **false**.