evaluate the indicated function for f(x)=xraise to power2+1 and g(x)=x-4  question:(f/g)(-1)-g(3) divide the result f(x) and g(x) together not one by one

We are given two functions:

\[
f(x) = x^2 + 1
\]
\[
g(x) = x - 4
\]

The problem asks to evaluate \((f/g)(-1) - g(3)\), where \(f/g\) represents the division of the functions \(f(x)\) and \(g(x)\) together.

### Step 1: Calculate \((f/g)(x)\)
We divide the two functions:
\[
\frac{f(x)}{g(x)} = \frac{x^2 + 1}{x - 4}
\]

### Step 2: Evaluate \((f/g)(-1)\)
Substitute \(x = -1\) into the expression \(\frac{f(x)}{g(x)}\):

\[
f(-1) = (-1)^2 + 1 = 1 + 1 = 2
\]
\[
g(-1) = -1 - 4 = -5
\]

Thus, 
\[
(f/g)(-1) = \frac{2}{-5} = -\frac{2}{5}
\

Evaluate the indicated function for f(x) = x^2 + 1 and g(x) = x - 4. The question is: (f/g)(-1) - g(3), dividing the result of f(x) and g(x) together, not one by one.

Learn how to evaluate the rational function (f/g)(x) for f(x) = x^2 + 1 and g(x) = x - 4. This problem involves algebraic concepts of dividing functions and evaluating them at specific values of x. Perfect for students in Grades 9-11.

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