Answer:
(g ° h)(-3) = 8/5 ⇒ first answer
Step-by-step explanation:
* Lets explain the meaning of the composition of functions
- Composition of functions is when one function is inside of an another
function
# If g(x) and h(x) are two functions, then (g ° h)(x) means h(x) is inside
g(x) and (h ° g)(x) means g(x) is inside h(x)
* Now lets solve the problem
∵ g(x) = [tex]\frac{x+1}{x-2}[/tex]
∵ h(x) = 4 - x
∵ (g ° h)(x) means h(x) is inside g(x)
- Find (g ° h)(-3) means find h(-3) at first and then replace the value of
h(-3) by the x of g(x)
* Lets find h(-3)
∵ h(x) = 4 - x
- Replace the x by -3
∴ h(-3) = 4 - (-3) = 4 + 3 = 7
- Now find g(7), means replace x by 7
∵ g(x) = [tex]\frac{x+1}{x-2}[/tex]
∴ g(7) = [tex]\frac{7+1}{7-2}=\frac{8}{5}[/tex]
∴ (g ° h)(-3) = 8/5
