Question

Help see picture attached

Answer 1

The answers are:

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

Answer 2

The correct answers are:
(1) $\sqrt{3} - 3$ ↔ (g+f)(2)
(2) 0 ↔  ($\frac{f}{g}$)(-1)
(3) $-3 * \sqrt{3}$ ↔ (g x f)(2)
(4) $( \sqrt{15})$ ↔ (g-f)(-1)

Explanation:
Box-1:
Step 1: Find (g + f)
$( \sqrt{11 - 4x} + 1 - x^2)$ --- (1)

Step 2: Now Plug in x = 2 in (1) gives you (g+f)(2):
$( \sqrt{11 - 4*2} + 1 - 2^2)$
=> $\sqrt{3} - 3$

Box-2:
Step 1: Find ($\frac{f}{g}$)
$\frac{1-x^2}{ \sqrt{11 - 4x} }$ --- (2)

Step 2: Now Plug in x = -1 in (2) gives you ($\frac{f}{g}$)(-1):
$\frac{1-(-1)^2}{ \sqrt{11 - 4(-1)} } \\ \frac{0}{ \sqrt{15} } \\ 0$

Box-3:
Step 1: Find (f x g)
$(1-x^2) * ({ \sqrt{11 - 4x} })$ --- (3)

Step 2: Now Plug in x = 2 in (3) gives you (g x f)(2):
$(1-(2)^2) * ({ \sqrt{11 - 4(2)} }) \\ -3 * \sqrt{3}$

Box-4:
Step-1: Find (g-f):
$( \sqrt{11 - 4x} - 1 + x^2)$ --- (4)
Step 2: Now Plug in x = -1 in (4) gives you (g-f)(-1):
$( \sqrt{11 - 4(-1)} - 1 + (-1)^2) \\ ( \sqrt{15} - 1 + 1) \\ ( \sqrt{15})$