Question

If g(x)=x+1/x-2 and h(x) = 4 – x, what is the value of (gxh) (-3)

Answer 1

For this case we have the following functions:

$g (x) = \frac {x + 1} {x-2}\\h (x) = 4-x$

We must find (g * h) (x)

By definition we have to:

$(g * h) (x) = g (x) * h (x)$

So:

$(g * h) (x) = \frac {(x + 1) (4-x)} {x-2}$

Now, we evaluate the function at x = -3:

$(g * h) (- 3) = \frac {(- 3 + 1) (4 - (- 3))} {- 3-2}\\(g * h) (- 3) = \frac {(- 2) (4 + 3)} {- 5}\\(g * h) (- 3) = \frac {(- 2) (7)} {- 5}\\(g * h) (- 3) = \frac {-14} {- 5}\\(g * h) (- 3) = \frac {14} {5}$

Answer:

$(g * h) (- 3) = \frac {14} {5}$