makasih ya sm yg udah nolong
Penjelasan dengan langkah-langkah:
[tex]f(x) = {x}^{2} + x \\ g(x) = \frac{2}{x + 3} \\ \\ a. \: (f + g)(x) = {x}^{2} + x + \frac{2}{x + 3} \\ = \frac{{x}^{2} (x + 3) + x(x + 3) + 2 }{x - 3} \\ = \frac{ {x}^{3} + 3 {x}^{2} + {x}^{2} + 3x + 2 }{x + 3} \\ = \frac{ {x}^{3} + 4 {x}^{2} + 3x + 2 }{x + 3} \\ \\ (f + g)(x - 3) = \frac{ {(x - 3)}^{3} + 4 {(x - 3)}^{2} + 3(x - 3) + 2 }{(x - 3) + 3} \\ = \frac{( {x}^{2} - 6x + 9)(x - 3) + 4( {x}^{2} - 6x + 9) + 3x - 9 + 2 }{x} \\ = \frac{ {x}^{3} - 3 {x}^{2} - 6 {x}^{2} + 18x + 9x - 27 + 4 {x}^{2} - 24x + 9 + 3x - 7}{x} \\ = \frac{ {x}^{3} - 5 {x}^{2} + 3x - 25 }{x} \\ = {x}^{2} - 5x + 3 - \frac{25}{x} [/tex]
[tex]b. \: (2f - 5g)(x) = 2( {x}^{2} + x) - 5( \frac{2}{x + 3}) \\ = 2 {x}^{2} + x - \frac{10}{x + 3} \\ = \frac{2 {x}^{2}(x + 3) + x(x + 3) - 10 }{x + 3} \\ = \frac{2 {x}^{3} + 6 {x}^{2} + {x}^{2} + 3x - 10 }{x + 3} \\ = \frac{2 {x}^{3} + 7 {x}^{2} + 3x - 10 }{x + 3} \\ \\ (2f - 5g)(2) = \frac{2 {(2)}^{3} + 7 ({2})^{2} + 3(2) - 10 }{2 + 3} \\ = \frac{2(8) + 7(4) + 6 - 10}{5} \\ = \frac{16 + 28 + 6 - 10}{5} \\ = \frac{40}{5} \\ = 8 [/tex]
[tex]c. \: (f.g)(x) = ( {x}^{2} + x)( \frac{2}{x + 3} ) \\ = \frac{2 {x}^{2} + 2x}{x + 3} \\ \\ (f.g)( - 1) = \frac{2 { (- 1)}^{2} + 2( - 1)}{ - 1 + 3} \\ = \frac{2 - 2}{2} \\ = \frac{0}{2} \\ = 0 [/tex]
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