Question

directions: use this information to answer parts a, b, and c.
jackson wants to determine the x - values for which the two functions $f(x)=x^2 - 4x + 11$ and $g(x)=3x - 1$ are equal.

part a
which is an equation that can be used to solve the problem? explain your answer.

show hints

$\bigcirc$ $3x - 1 = 0$; the functions are equal when $g(x)=0$.
$\bigcirc$ $x^2 - 4x + 11 + 3x - 1 = 0$; the sum of the functions equals 0.
$\bigcirc$ $x^2 - 4x + 11 = 0$; the functions are equal when $f(x)=0$.
$\bigcirc$ $x^2 - 4x + 11 = 3x - 1$; the functions are equal when $f(x)=g(x)$.

Explanation:

To find the \( x \)-values where \( f(x) \) and \( g(x) \) are equal, we set \( f(x)=g(x) \). Given \( f(x) = x^2 - 4x + 11 \) and \( g(x)=3x - 1 \), equating them gives \( x^2 - 4x + 11=3x - 1 \). The other options are incorrect: the first option sets \( g(x) = 0 \) (not related to \( f(x)=g(x) \)), the second option sums the functions (not equate them), and the third option sets \( f(x)=0 \) (not related to \( g(x) \)).

Answer:

D. \( x^2 - 4x + 11 = 3x - 1 \); The functions are equal when \( f(x) = g(x) \)