Math  /  Algebra

Questionf(x)=5x24g(x)=3x1\begin{array}{l} f(x)=5 x^{2}-4 \\ g(x)=\sqrt{3 x-1} \end{array}
Find fgf \cdot g and fgf-g. Then, give their domains using interval notation. (fg)(x)=(f \cdot g)(x)= \square
Domain of fgf \cdot g : \square (fg)(x)=(f-g)(x)= \square
Domain of fgf-g : \square

Studdy Solution
(fg)(x)=(5x24)3x1(f \cdot g)(x) = (5x^2 - 4)\sqrt{3x - 1}
Domain of fgf \cdot g: [13,)\left[ \frac{1}{3}, \infty \right)
(fg)(x)=(5x24)3x1(f - g)(x) = (5x^2 - 4) - \sqrt{3x - 1}Domain of fgf - g: [13,)\left[ \frac{1}{3}, \infty \right)

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