Question

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

•8/5
•5/2
•15/2
•18/5

Answer 1

a) For the given functions: (g.h)(-3) = 8/5

Explanation:

Here, the given functions are:
`g(x) =(x+1)/(x-2)     , h(x)  =  4 - x`

To find the value of (g.h)(-3)

Now, g.h(x) = g (h(x))

⇒ g (h(x)) = g (4 - x)

or,
`g(4-x)  = ((4-x)+1)/((4-x)-2)  = (5-x)/(2 - x)`

⇒
`g (h(x))  = (5-x)/(2 - x)`

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

Hence, for the given functions: (g.h)(-3) = 8/5