Questions: Consider the function: g(x)=x^2-7 x+13 Find and simplify g(x-11). [Hint: See § 2.1, Example 5d.]

Solution Steps

To find and simplify $g(x-11)$, substitute $x-11$ into the function $g(x) = x^2 - 7x + 13$. This involves replacing every instance of $x$ in the function with $x-11$ and then simplifying the resulting expression.

We start with the function $g(x) = x^2 - 7x + 13$. To find $g(x-11)$, we substitute $x-11$ for $x$:

$$g(x-11) = (x-11)^2 - 7(x-11) + 13$$

Next, we expand the expression:

$$g(x-11) = (x^2 - 22x + 121) - (7x - 77) + 13$$

This simplifies to:

$$g(x-11) = x^2 - 22x + 121 - 7x + 77 + 13$$

Now, we combine the like terms:

$$g(x-11) = x^2 - 29x + (121 + 77 + 13)$$

Calculating the constant term:

$$121 + 77 + 13 = 211$$

Thus, we have:

$$g(x-11) = x^2 - 29x + 211$$

Final Answer