Question

If g (x) = StartFraction x + 1 Over x minus 2 EndFraction and h(x) = 4 – x, what is the value of (g circle h) (negative 3)?

Answer 1

The answer is 8/5

Explanation:

Answer 2

`(8)/(5)`

Explanation:

Given that
`g(x) = (x + 1)/(x - 2)` and h(x) = 4 - x

Now, if y = f(x) and y = g(x) then the composite function (f∘g)(x) is given by f[g(x)].

Hence, (g∘h)(x) =
`g[h(x)] = ((4 - x) + 1)/((4 - x) - 2) = (5 - x)/(2 - x)` .......... (1)

Now, from equation (1) we get,

(g∘h)(x) =
`(5 - x)/(2 - x)`

⇒ (g∘h)(- 3) =
`(5 - ( - 3))/(2 - ( - 3)) = (8)/(5)` (Answer)