Math  /  Algebra

QuestionSuppose that the functions ff and gg are defined for all real numbers xx as follows. f(x)=x4g(x)=4x+1\begin{array}{l} f(x)=x-4 \\ g(x)=4 x+1 \end{array}
Write the expressions for (gf)(x)(g-f)(x) and (gf)(x)(g \cdot f)(x) and evaluate (g+f)(3)(g+f)(3). (gf)(x)=(gf)(x)=(g+f)(3)=\begin{array}{r} (g-f)(x)=\square \\ (g \cdot f)(x)=\square \\ (g+f)(3)=\square \end{array}

Studdy Solution
(gf)(x)=3x+5(g-f)(x) = 3x + 5 (gf)(x)=4x215x4(g \cdot f)(x) = 4x^2 - 15x - 4 (g+f)(3)=12(g+f)(3) = 12

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