Question
If \( f(x)=6 x \) and \( g(x)=2 x-7 \), find \( (f g)(x) \) \( (\mathrm{fg})(\mathrm{x})=\square \)
Ask by Curry Chang. in the United States
Mar 12,2025
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Answer
\((fg)(x) = 12x^2 - 42x\)
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Bonus Knowledge
To find \( (f g)(x) \), you need to multiply the functions \( f(x) \) and \( g(x) \) together. Start by substituting the given functions: \[ f(x) = 6x \quad \text{and} \quad g(x) = 2x - 7. \] Now, calculate \( (f g)(x) = f(x) \cdot g(x) \): \[ (f g)(x) = (6x)(2x - 7). \] Next, distribute \( 6x \) across \( (2x - 7) \): \[ (f g)(x) = 6x \cdot 2x - 6x \cdot 7 = 12x^2 - 42x. \] So, we have: \[ (f g)(x) = 12x^2 - 42x. \]