`f(x)=7x-3`
`g(x)=x^(2)-2x+6`
The function f and g are defined abvoe. What is the value of `f(11)-g(4)`?

Answer

To find the value of \( f(11) - g(4) \), we will first calculate \( f(11) \) and then \( g(4) \).

### Step 1: Calculate \( f(11) \)

The function \( f(x) \) is given by:
\[ f(x) = 7x - 3 \]

Now, substitute \( x = 11 \):
\[ f(11) = 7(11) - 3 \]
\[ f(11) = 77 - 3 \]
\[ f(11) = 74 \]

### Step 2: Calculate \( g(4) \)

The function \( g(x) \) is given by:
\[ g(x) = x^2 - 2x + 6 \]

Now, substitute \( x = 4 \):
\[ g(4) = 4^2 - 2(4) + 6 \]
\[ g(4) = 16 - 8 + 6 \]
\[ g(4) = 14 \]

### Step 3: Calculate \( f(11) - g(4) \)

Now that we have both values, we can find \( f(11) - g(4) \):
\[ f(11) - g(4) = 74 - 14 \]
\[ f(11) - g(4) = 60 \]

Thus, the final answer is:
\[ \boxed{60} \]