Question

Help see picture attached

Answer 1

The correct answers are:
(1)
`√(3) - 3` ↔ (g+f)(2)
(2) 0 ↔ (
`(f)/(g)`)(-1)
(3)
`-3 * √(3)` ↔ (g x f)(2)
(4)
`( √(15))` ↔ (g-f)(-1)

Step-by-step explanation:
Box-1:
Step 1: Find (g + f)

`( √(11 - 4x) + 1 - x^2)` --- (1)

Step 2: Now Plug in x = 2 in (1) gives you (g+f)(2):

`( √(11 - 4*2) + 1 - 2^2)`
=>
`√(3) - 3`

Box-2:
Step 1: Find (
`(f)/(g)`)

`(1-x^2)/( √(11 - 4x) )` --- (2)

Step 2: Now Plug in x = -1 in (2) gives you (
`(f)/(g)`)(-1):

`(1-(-1)^2)/( √(11 - 4(-1)) ) \\ (0)/( √(15) ) \\ 0`

Box-3:
Step 1: Find (f x g)

`(1-x^2) * ({ √(11 - 4x) })` --- (3)

Step 2: Now Plug in x = 2 in (3) gives you (g x f)(2):

`(1-(2)^2) * ({ √(11 - 4(2)) }) \\ -3 * √(3)`

Box-4:
Step-1: Find (g-f):

`( √(11 - 4x) - 1 + x^2)` --- (4)
Step 2: Now Plug in x = -1 in (4) gives you (g-f)(-1):

`( √(11 - 4(-1)) - 1 + (-1)^2) \\ ( √(15) - 1 + 1) \\ ( √(15))`

Answer 2

The answers are:

\sqrt{3}-3 ------> (g+f)(2)
0 ------> (f/g)(-1)
-3(sqrt)(3) ------> (gxf)(2)
(sqrt)(15) ------> (g-f)(-1)