If `f(x)=7x^(4)-2x^(3)-8x-5` find f(-1)

Answer

To find \( f(-1) \) for the function \( f(x) = 7x^4 - 2x^3 - 8x - 5 \), we will substitute \( x = -1 \) into the function and simplify step by step.

### Step-by-step Solution:

1. **Substitute \( x = -1 \) into the function:**
\[ f(-1) = 7(-1)^4 - 2(-1)^3 - 8(-1) - 5 \]

2. **Calculate \( (-1)^4 \):**
\[ (-1)^4 = 1 \]
Therefore,
\[ 7(-1)^4 = 7 \cdot 1 = 7 \]

3. **Calculate \( (-1)^3 \):**
\[ (-1)^3 = -1 \]
Therefore,
\[ -2(-1)^3 = -2 \cdot (-1) = 2 \]

4. **Calculate \( -8(-1) \):**
\[ -8(-1) = 8 \]

5. **Combine all the calculated values:**
\[ f(-1) = 7 + 2 + 8 - 5 \]

6. **Perform the addition and subtraction:**
\[ 7 + 2 = 9 \]
\[ 9 + 8 = 17 \]
\[ 17 - 5 = 12 \]

7. **Final result:**
\[ f(-1) = 12 \]

### Final Answer:
\[ f(-1) = 12 \]