Question
The functions \( f \) and \( g \) are defined as follows, \[ f(x)=-4 x+2 \quad g(x)=3 x^{2}-3 x \] Find \( f(6) \) and \( g(-3) \), Simplify your answers as much as possible, \( f(6)=\square \)
Ask by Watson Estrada. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f(6) = -22 \) and \( g(-3) = 36 \).
Solution
Calculate or simplify the expression \( -4*6+2 \).
Calculate the value by following steps:
- step0: Calculate:
\(-4\times 6+2\)
- step1: Multiply the numbers:
\(-24+2\)
- step2: Add the numbers:
\(-22\)
Calculate or simplify the expression \( 3*(-3)^{2}-3*(-3) \).
Calculate the value by following steps:
- step0: Calculate:
\(3\left(-3\right)^{2}-3\left(-3\right)\)
- step1: Multiply the terms:
\(3^{3}-3\left(-3\right)\)
- step2: Multiply the numbers:
\(3^{3}+9\)
- step3: Evaluate the power:
\(27+9\)
- step4: Add the numbers:
\(36\)
The value of \( f(6) \) is -22 and the value of \( g(-3) \) is 36.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
To find \( f(6) \), we substitute \( 6 \) into the function \( f(x) \): \[ f(6) = -4(6) + 2 = -24 + 2 = -22 \] So, \( f(6) = -22 \). Now for \( g(-3) \), we substitute \( -3 \) into the function \( g(x) \): \[ g(-3) = 3(-3)^{2} - 3(-3) = 3(9) + 9 = 27 + 9 = 36 \] Thus, \( g(-3) = 36 \). So the final answers are: \( f(6) = -22 \) and \( g(-3) = 36 \).
