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)

Answer 1

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

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

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

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

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