Answer:
a) [tex]h = -\frac{7}{4}[/tex], b) [tex]h = f\,\circ\,g (-5) = \frac{3}{2}[/tex], c) [tex]h = g\,\circ\,f (-2) = \frac{3}{8}[/tex]
Step-by-step explanation:
We proceed to solve each exercise below:
a) [tex]f(-2) +3\cdot g(0)[/tex]
[tex]h = \frac{2\cdot (-2)}{3\cdot (-2)+5}+3\cdot \left(\frac{3}{0+4} \right)[/tex]
[tex]h = \frac{-4}{-6+5} +3\cdot \left(\frac{3}{4} \right)[/tex]
[tex]h = -4+\frac{9}{4}[/tex]
[tex]h = \frac{-16+9}{4}[/tex]
[tex]h = -\frac{7}{4}[/tex]
b) [tex]h = f\,\circ \,g (-5)[/tex]
[tex]h = f\,\circ\,g (x) = \frac{\frac{6}{x+4} }{\frac{9}{x+4}+5 }[/tex]
[tex]h = f\,\circ\,g (x)= \frac{\frac{6}{x+4} }{\frac{9+5\cdot (x+4)}{x+4} }[/tex]
[tex]h = f\,\circ\,g (x) = \frac{6}{29+5\cdot x}[/tex]
[tex]h = f\,\circ\,g (-5) = \frac{6}{29+5\cdot (-5)}[/tex]
[tex]h = f\,\circ\,g (-5) = \frac{3}{2}[/tex]
c) [tex]h = g\,\circ\,f(-2)[/tex]
[tex]h = g\,\circ \, f (x) = \frac{3}{\frac{2\cdot x}{3\cdot x + 5} + 4 }[/tex]
[tex]h = g\,\circ\,f (x) = \frac{3}{\frac{2\cdot x +4\cdot (3\cdot x +5)}{3\cdot x +5 } }[/tex]
[tex]h = g\,\circ \,f (x) = \frac{3\cdot (3\cdot x +5)}{2\cdot x +12\cdot x +20}[/tex]
[tex]h = g\,\circ\,f(x) = \frac{9\cdot x +15}{14\cdot x +20}[/tex]
[tex]h = g\,\circ\,f(-2) = \frac{9\cdot (-2)+15}{14\cdot (-2)+20}[/tex]
[tex]h = g\,\circ\,f (-2) = \frac{-3}{-8}[/tex]
[tex]h = g\,\circ\,f (-2) = \frac{3}{8}[/tex]
