If `f(x)=x^(3)-4x+8`, then f(5)=

Options

A. `67`
B. `97`
C. `113`
D. `147`

Answer

To find the value of \( f(5) \) for the function \( f(x) = x^3 - 4x + 8 \), we will substitute \( x \) with \( 5 \) in the function.

### Step-by-Step Solution:

1. **Write down the function**:
The given function is
\[ f(x) = x^3 - 4x + 8 \]

2. **Substitute \( x \) with \( 5 \)**:
We need to find \( f(5) \), so we substitute \( x \) with \( 5 \):
\[ f(5) = 5^3 - 4 \cdot 5 + 8 \]

3. **Calculate \( 5^3 \)**:
Calculate \( 5^3 \):
\[ 5^3 = 125 \]

4. **Calculate \( -4 \cdot 5 \)**:
Now calculate \( -4 \cdot 5 \):
\[ -4 \cdot 5 = -20 \]

5. **Combine the results**:
Now substitute these values back into the equation:
\[ f(5) = 125 - 20 + 8 \]

6. **Perform the addition and subtraction**:
First, perform the subtraction:
\[ 125 - 20 = 105 \]
Then add \( 8 \):
\[ 105 + 8 = 113 \]

7. **Final result**:
Therefore,
\[ f(5) = 113 \]

### Final Answer:
\[ f(5) = 113 \]