Answer:
The three errors are:
1) Incorrectly swapping the variables x and y.
2) Failure to use the ± symbol.
3) The domain is wrong; it should be x ≤ 0.
Step-by-step explanation:
Review the following steps.

Step 1: 
The initial step is incorrect because the variables x and y were switched improperly; it should be:

Step 2: 
Step 3: 
Step 4:
, for x ≥ 0
Step 4 contains an error as the ± sign is required. Additionally, the function's domain is inaccurately stated.
The radicand must be nonnegative, implying that x must satisfy x ≤ 0.
Step One
Deduct 32 from both sides.
F - 32 = \frac{9}{5}(k - 273.15)
Step Two
Multiply each side by \frac{5}{9}.
\frac{5}{9}(F - 32) = \frac{5}{9} \times \frac{9}{5}(k - 273.15)
\frac{5}{9}(F - 32) = k - 273.15
Step Three
Add 273.15 to both sides.
\frac{5}{9}(F - 32) + 273.15 = k
Problem B
F = 180
Solve for k
k = \frac{5}{9}(F - 32) + 273.15
k = \frac{5}{9}(180 - 32) + 273.15
k = \frac{5}{9} \times 148 + 273.15
k = 82.2222 + 273.15
k = 355.3722
k = 355.4 <<< Answer
Approximately 2, I believe... I calculated it to be around 2.10.
Solution:
We know, g(x) = f(x) + k --------(1)
It is given that f(x) =
(x+2)
and g(x) =
(x+5)
Substituting f(x) and g(x) into equation (1):
→
(x+5) =
(x+2) + k
→
= k
→ k = 
Thus, the value of k is 1.