3. Given $$ f(x)=(x+3)(x-5) $$, determine the $$ x $$-intercepts fot $$ f\left(\frac{1}{3} x\right) $$

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UpStudy AI · Accepted Answer

To find the $$ x $$-intercepts of the function $$ f\left(\frac{1}{3} x\right) $$, follow these steps:

1. **Start with the given function:**
   $$
   f(x) = (x + 3)(x - 5)
   $$

2. **Substitute $$ \frac{1}{3} x $$ into the function:**
   $$
   f\left(\frac{1}{3} x\right) = \left(\frac{1}{3} x + 3\right) \left(\frac{1}{3} x - 5\right)
   $$

3. **Set the function equal to zero to find the $$ x $$-intercepts:**
   $$
   \left(\frac{1}{3} x + 3\right) \left(\frac{1}{3} x - 5\right) = 0
   $$

4. **Solve each factor for $$ x $$:**

- **First factor:**
     $$
     \frac{1}{3} x + 3 = 0 \
     \frac{1}{3} x = -3 \
     x = -9
     $$

- **Second factor:**
     $$
     \frac{1}{3} x - 5 = 0 \
     \frac{1}{3} x = 5 \
     x = 15
     $$

5. **Conclusion:**
   The $$ x $$-intercepts of $$ f\left(\frac{1}{3} x\right) $$ are at:
   $$
   (-9, 0) \quad \text{and} \quad (15, 0)
   $$

**Final Answer:**
The x-intercepts are at x = –9 and x = 15.
The x-intercepts are at x = –9 and x = 15.

3. Given \( f(x)=(x+3)(x-5) \), determine the \( x \)-intercepts fot \( f\left(\frac{1}{3} x\right) \)

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