Answer:
a) For the given functions: (g.h)(-3) = 8/5
Step-by-step explanation:
Here, the given functions are: [tex]g(x) =\frac{x+1}{x-2} , h(x) = 4 - x[/tex]
To find the value of (g.h)(-3)
Now, g.h(x) = g (h(x))
⇒ g (h(x)) = g (4 - x)
or, [tex]g(4-x) = \frac{(4-x)+1}{(4-x)-2} = \frac{5-x}{2 - x}[/tex]
⇒ [tex]g (h(x)) = \frac{5-x}{2 - x}[/tex]
⇒[tex]g (h(-3)) = \frac{5-(-3)}{2 - (-3)} = \frac{5 + 3}{2+3} = \frac{8}{5}[/tex]
Hence, for the given functions: (g.h)(-3) = 8/5
