if `f(x)=ax^7+bx^3+cx-5`, `f(-7) = 7` then `f(7)`is

Answer

To solve the problem, we need to find the value of \( f(7) \) given that \( f(x) = ax^7 + bx^3 + cx - 5 \) and \( f(-7) = 7 \).

### Step-by-Step Solution:

1. **Substitute -7 into the function**:
We start by substituting \( x = -7 \) into the function:
\[ f(-7) = a(-7)^7 + b(-7)^3 + c(-7) - 5 \]
Given that \( f(-7) = 7 \), we can set up the equation:
\[ a(-7)^7 + b(-7)^3 + c(-7) - 5 = 7 \]

2. **Calculate the powers of -7**:
Now, we calculate the powers:
\[ (-7)^7 = -7^7 \quad \text{(since the exponent is odd)} \]
\[ (-7)^3 = -7^3 \quad \text{(since the exponent is odd)} \]
Thus, we can rewrite the equation:
\[ -a(7^7) - b(7^3) - 7c - 5 = 7 \]

3. **Rearranging the equation**:
Adding 5 to both sides gives:
\[ -a(7^7) - b(7^3) - 7c = 12 \]

4. **Multiply through by -1**:
To simplify, we multiply the entire equation by -1:
\[ a(7^7) + b(7^3) + 7c = -12 \]

5. **Finding \( f(7) \)**:
Now, we substitute \( x = 7 \) into the function:
\[ f(7) = a(7^7) + b(7^3) + c(7) - 5 \]

6. **Using the previous result**:
From step 4, we know:
\[ a(7^7) + b(7^3) + 7c = -12 \]
Therefore, we can substitute this into the equation for \( f(7) \):
\[ f(7) = (-12 - 7c) + 7c - 5 \]

7. **Simplifying**:
The \( 7c \) terms cancel out:
\[ f(7) = -12 - 5 = -17 \]

### Final Answer:
Thus, the value of \( f(7) \) is:
\[ \boxed{-17} \]