The function f is such that f(x) = 2x/3x+5 The function g is such that g(x) = 3/x+4 Find fg(-5)

Question

The function f is such that f(x) = 2x/3x+5 The function g is such that g(x) = 3/x+4 Find fg(-5)

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Helga 4 months 2021-09-05T07:08:49+00:00 1 Answers 4 views 0

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    2021-09-05T07:10:20+00:00

    Answer:

    f(g(-5)) = \frac{3}{2}

    Step-by-step explanation:

    Given

    f(x) = \frac{2x}{3x+5}

    g(x) = \frac{3}{x+4}

    Required

    Find f(g(-5))

    First, we calculate f(g(x))

    f(x) = \frac{2x}{3x+5}

    Substitute g(x) for x

    f(g(x)) = \frac{2g(x)}{3g(x) + 5}

    Substitute \frac{3}{x+4} for g(x)

    f(g(x)) = \frac{2*\frac{3}{x+4}}{3*\frac{3}{x+4} + 5}

    f(g(x)) = \frac{\frac{6}{x+4}}{\frac{9}{x+4} + 5}

    f(g(x)) = \frac{6}{x+4}/ (\frac{9}{x+4} + 5})

    Take LCM

    f(g(x)) = \frac{6}{x+4}/ \frac{9+5x+20}{x+4}}

    f(g(x)) = \frac{6}{x+4}/ \frac{5x+29}{x+4}}

    Rewrite as multiplication

    f(g(x)) = \frac{6}{x+4}* \frac{x+4}{5x+29}}

    f(g(x)) = \frac{6}{5x+29}

    Substitute -5 for x

    f(g(-5)) = \frac{6}{-5*5+29}

    f(g(-5)) = \frac{6}{-25+29}

    f(g(-5)) = \frac{6}{4}

    f(g(-5)) = \frac{3}{2}

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