Answered

For the given functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex], find the indicated composition.

[tex]\( f(x) = 10x^2 - 8x \)[/tex]

[tex]\( g(x) = 7x - 3 \)[/tex]

Find [tex]\( (f \circ g)(11) \)[/tex].

A. 54,168
B. 83,028
C. 46,317
D. 7,851



Answer :

GinnyAnswer
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.

Other Questions