Let's solve the problem step-by-step:
1. Identify the functions:
[tex]\( f(x) = 10x^2 - 8x \)[/tex]
[tex]\( g(x) = 7x - 3 \)[/tex]
2. Find [tex]\( g(11) \)[/tex]:
Substitute [tex]\( x = 11 \)[/tex] into [tex]\( g(x) \)[/tex]:
[tex]\[
g(11) = 7 \cdot 11 - 3
\][/tex]
Perform the multiplication and subtraction:
[tex]\[
g(11) = 77 - 3 = 74
\][/tex]
3. Use the result of [tex]\( g(11) \)[/tex] to find [tex]\( f(g(11)) \)[/tex]:
Substitute [tex]\( x = 74 \)[/tex] into [tex]\( f(x) \)[/tex]:
[tex]\[
f(74) = 10 \cdot 74^2 - 8 \cdot 74
\][/tex]
Calculate [tex]\( 74^2 \)[/tex]:
[tex]\[
74^2 = 5476
\][/tex]
Now, multiply by 10:
[tex]\[
10 \cdot 5476 = 54760
\][/tex]
Next, calculate [tex]\( 8 \cdot 74 \)[/tex]:
[tex]\[
8 \cdot 74 = 592
\][/tex]
Finally, subtract the second result from the first:
[tex]\[
f(74) = 54760 - 592 = 54168
\][/tex]
4. Conclusion:
So, the value of [tex]\((f \circ g)(11)\)[/tex] is 54168.
Therefore, the correct answer is:
[tex]\[
\boxed{54,168}
\][/tex]
Thus, the indicated composition [tex]\((f \circ g)(11)\)[/tex] evaluates to 54168, making option (A) the correct choice.
