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Find an expression for:(𝑓𝑔)(𝑥)( gf​ )(x)left parenthesis, start fraction, f, divided by, g, end fraction, right parenthesis, left parenthesis, x, right parenthesisGiven the functions:𝑓(𝑥)=5𝑥+1𝑔(𝑥)=3𝑥−1f(x)g(x)​ =5x+1=3x−1​

Question

Find an expression for:(𝑓𝑔)(𝑥)( gf​ )(x)left parenthesis, start fraction, f, divided by, g, end fraction, right parenthesis, left parenthesis, x, right parenthesisGiven the functions:𝑓(𝑥)=5𝑥+1𝑔(𝑥)=3𝑥−1f(x)g(x)​ =5x+1=3x−1​

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Solution

Para encontrar una expresión para (fg)(x)(\frac{f}{g})(x), dados los funciones f(x)=5x+1f(x) = 5x + 1 y g(x)=3x1g(x) = 3x - 1, sigue estos pasos:

  1. Escribe la expresión de f(x)g(x)\frac{f(x)}{g(x)}: (fg)(x)=f(x)g(x) \left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)}

  2. Sustituye f(x)f(x) y g(x)g(x) con sus respectivas funciones: (fg)(x)=5x+13x1 \left(\frac{f}{g}\right)(x) = \frac{5x + 1}{3x - 1}

Por lo tanto, la expresión para (fg)(x)(\frac{f}{g})(x) es: (fg)(x)=5x+13x1 \left(\frac{f}{g}\right)(x) = \frac{5x + 1}{3x - 1}

This problem has been solved

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