Answer:
[tex]f(g(-5)) = \frac{3}{2}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{2x}{3x+5}[/tex]
[tex]g(x) = \frac{3}{x+4}[/tex]
Required
Find f(g(-5))
First, we calculate f(g(x))
[tex]f(x) = \frac{2x}{3x+5}[/tex]
Substitute g(x) for x
[tex]f(g(x)) = \frac{2g(x)}{3g(x) + 5}[/tex]
Substitute [tex]\frac{3}{x+4}[/tex] for g(x)
[tex]f(g(x)) = \frac{2*\frac{3}{x+4}}{3*\frac{3}{x+4} + 5}[/tex]
[tex]f(g(x)) = \frac{\frac{6}{x+4}}{\frac{9}{x+4} + 5}[/tex]
[tex]f(g(x)) = \frac{6}{x+4}/ (\frac{9}{x+4} + 5})[/tex]
Take LCM
[tex]f(g(x)) = \frac{6}{x+4}/ \frac{9+5x+20}{x+4}}[/tex]
[tex]f(g(x)) = \frac{6}{x+4}/ \frac{5x+29}{x+4}}[/tex]
Rewrite as multiplication
[tex]f(g(x)) = \frac{6}{x+4}* \frac{x+4}{5x+29}}[/tex]
[tex]f(g(x)) = \frac{6}{5x+29}[/tex]
Substitute -5 for x
[tex]f(g(-5)) = \frac{6}{-5*5+29}[/tex]
[tex]f(g(-5)) = \frac{6}{-25+29}[/tex]
[tex]f(g(-5)) = \frac{6}{4}[/tex]
[tex]f(g(-5)) = \frac{3}{2}[/tex]
