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Marina86 [1]
3 years ago
7

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)

Mathematics
1 answer:
White raven [17]3 years ago
5 0

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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