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