After substituting $x=2$, focus first on simplifying 2^2 - 4m{\times}2 + 7. Do not worry about the other parentheses until this one is simplified.

For 3 - \tfrac12 m{\times} 2, make sure you multiply by $1/2$ before subtracting, and pay attention to the minus sign in front of $1/2$.

Once both parentheses are simplified to single numbers, multiply those two numbers to get the value of $g(2)$.

Type g(x) = (x^2 - 4x + 7)(3 - 1/2 x) into a new Desmos line so Desmos defines the function $g$.

In a new line, type g(2) and look at the numerical value Desmos displays; that value is the correct value of $g(2)$.

Start with the definition of the function:

To find $g(2)$, replace every $x$ with $2$:

Now simplify the expression 2^2 - 4m{\times}2 + 7 step by step:

• $2^2 = 4$
• 4m{\times}2 = 8

So

Compute this:

• $4 - 8 = -4$
• $-4 + 7 = 3$

So the first factor becomes $3$.

Next simplify 3 - \tfrac12 m{\times} 2:

• \tfrac12 m{\times} 2 = 1

So

Now the expression for $g(2)$ is

Finally, multiply the two simplified factors:

• 3 m{\times} 2 = 6

So

This corresponds to answer choice B) 6.