Question
If f(x)=16x3−7
and g(x)=11−12x
, then g(f(x))
can be represented by which of the following?(1 point)
Responses
4−12(16x3)
4 minus Start Fraction 1 over 2 End Fraction left parenthesis Start Fraction 16 x over 3 End Fraction right parenthesis
11−12(16x3−7)
11 minus Start Fraction 1 over 2 End Fraction left parenthesis Start Fraction 16 x over 3 End Fraction minus 7 right parenthesis
11−16(12x)3−7
11 minus Start Fraction 16 left parenthesis Start Fraction 1 over 2 End Fraction x right parenthesis over 3 End Fraction minus 7
16(11−12x)3−7
and g(x)=11−12x
, then g(f(x))
can be represented by which of the following?(1 point)
Responses
4−12(16x3)
4 minus Start Fraction 1 over 2 End Fraction left parenthesis Start Fraction 16 x over 3 End Fraction right parenthesis
11−12(16x3−7)
11 minus Start Fraction 1 over 2 End Fraction left parenthesis Start Fraction 16 x over 3 End Fraction minus 7 right parenthesis
11−16(12x)3−7
11 minus Start Fraction 16 left parenthesis Start Fraction 1 over 2 End Fraction x right parenthesis over 3 End Fraction minus 7
16(11−12x)3−7
Answers
GPT-4o mini
To find \( g(f(x)) \) where \( f(x) = 16x^3 - 7 \) and \( g(x) = 11 - 12x \), we will substitute \( f(x) \) into \( g(x) \).
1. Start by expressing \( g(f(x)) \):
\[
g(f(x)) = g(16x^3 - 7)
\]
2. Now replace \( x \) in \( g(x) \) with \( 16x^3 - 7 \):
\[
g(16x^3 - 7) = 11 - 12(16x^3 - 7)
\]
3. Now simplify \( g(16x^3 - 7) \):
\[
g(16x^3 - 7) = 11 - 12 \cdot 16x^3 + 12 \cdot 7
\]
\[
= 11 - 192x^3 + 84
\]
\[
= 95 - 192x^3
\]
We can now review the available choices to see which one matches \( 95 - 192x^3 \).
None of the choices provided directly match \( 95 - 192x^3 \), but the choice that aligns closely if we consider moving terms around might be:
- **11 − 12(16x³ − 7)**, which directly corresponds with our simplification before breaking it down.
However, ultimately, the actual end result is \( 95 - 192x^3 \), which is the correct representation for \( g(f(x)) \). Thus if you were to express it correctly based on the function outputs, it would be represented as:
**None of the answers exactly match what \( g(f(x)) \) evaluates to**, which is \( 95 - 192x^3 \).
In conclusion, if your options included a direct format or simplified version of \( 95 - 192x^3\), that would be the correct expression for \( g(f(x)) \).
1. Start by expressing \( g(f(x)) \):
\[
g(f(x)) = g(16x^3 - 7)
\]
2. Now replace \( x \) in \( g(x) \) with \( 16x^3 - 7 \):
\[
g(16x^3 - 7) = 11 - 12(16x^3 - 7)
\]
3. Now simplify \( g(16x^3 - 7) \):
\[
g(16x^3 - 7) = 11 - 12 \cdot 16x^3 + 12 \cdot 7
\]
\[
= 11 - 192x^3 + 84
\]
\[
= 95 - 192x^3
\]
We can now review the available choices to see which one matches \( 95 - 192x^3 \).
None of the choices provided directly match \( 95 - 192x^3 \), but the choice that aligns closely if we consider moving terms around might be:
- **11 − 12(16x³ − 7)**, which directly corresponds with our simplification before breaking it down.
However, ultimately, the actual end result is \( 95 - 192x^3 \), which is the correct representation for \( g(f(x)) \). Thus if you were to express it correctly based on the function outputs, it would be represented as:
**None of the answers exactly match what \( g(f(x)) \) evaluates to**, which is \( 95 - 192x^3 \).
In conclusion, if your options included a direct format or simplified version of \( 95 - 192x^3\), that would be the correct expression for \( g(f(x)) \).