Let's solve the problem step by step.
We are given two functions:
[tex]\[ f(x) = 3x^2 - 1 \][/tex]
[tex]\[ g(x) = -2x + 7 \][/tex]
And we need to calculate [tex]\( f(x) + g(x) - 3 \)[/tex] for a particular value of [tex]\( x \)[/tex]. In this case, [tex]\( x = 3 \)[/tex].
First, let's find [tex]\( f(x) \)[/tex] when [tex]\( x = 3 \)[/tex]:
[tex]\[ f(3) = 3(3)^2 - 1 \][/tex]
[tex]\[ f(3) = 3 \cdot 9 - 1 \][/tex]
[tex]\[ f(3) = 27 - 1 \][/tex]
[tex]\[ f(3) = 26 \][/tex]
Next, let's find [tex]\( g(x) \)[/tex] when [tex]\( x = 3 \)[/tex]:
[tex]\[ g(3) = -2(3) + 7 \][/tex]
[tex]\[ g(3) = -6 + 7 \][/tex]
[tex]\[ g(3) = 1 \][/tex]
Now, we can calculate [tex]\( f(3) + g(3) - 3 \)[/tex]:
[tex]\[ f(3) + g(3) - 3 = 26 + 1 - 3 \][/tex]
[tex]\[ f(3) + g(3) - 3 = 27 - 3 \][/tex]
[tex]\[ f(3) + g(3) - 3 = 24 \][/tex]
Therefore, the answer is not one of the given options. Let's revisit the answer choices to confirm.
\- 39
\- 27
\- -14
\- -41
Since 24 is not among the provided options, it is likely that there was an error either in the problem's question or in the provided answer choices. The correct calculation, however, yields:
[tex]\[ \boxed{24} \][/tex]
