For this case we have the following functions:
[tex]g (x) = \frac {x + 1} {x-2}\\h (x) = 4-x[/tex]
We must find (g * h) (x)
By definition we have to:
[tex](g * h) (x) = g (x) * h (x)[/tex]
So:
[tex](g * h) (x) = \frac {(x + 1) (4-x)} {x-2}[/tex]
Now, we evaluate the function at x = -3:
[tex](g * h) (- 3) = \frac {(- 3 + 1) (4 - (- 3))} {- 3-2}\\(g * h) (- 3) = \frac {(- 2) (4 + 3)} {- 5}\\(g * h) (- 3) = \frac {(- 2) (7)} {- 5}\\(g * h) (- 3) = \frac {-14} {- 5}\\(g * h) (- 3) = \frac {14} {5}[/tex]
Answer:
[tex](g * h) (- 3) = \frac {14} {5}[/tex]
