Let f(x)= 4 and g(x)= �ãx-2 :
X2 - 4
f o g(11)=ANSWER: Square root X-2/ 11-2 =�ã9=3 4/32 -4 = 4/5
f o f(0)=ANSWER
Determine the Domain of f o g=ANSWER:
To determine the value of f o g(11), we need to perform the following steps:
Step 1: Replace the variable x in g(x) with 11:
g(x) = √(x-2)
g(11) = √(11-2) = √9 = 3
Step 2: Substitute the result of g(11) into f(x):
f(x) = 4/(x²-4)
f o g(11) = f(g(11)) = f(3) = 4/(3²-4) = 4/(9-4) = 4/5
Therefore, f o g(11) = 4/5
To determine the value of f o f(0), we need to perform the following steps:
Step 1: Replace the variable x in f(x) with 0:
f(x) = 4/(x²-4)
f(0) = 4/(0²-4) = 4/(-4) = -1
Therefore, f o f(0) = -1
Now, let's determine the domain of f o g:
The domain of a composed function f o g is the set of all x values that are in the domain of g and produce a valid output that is in the domain of f.
In this case, the domain of g is all real numbers except for x = 2, since the expression √(x-2) requires x-2 to be non-negative.
The domain of f is all real numbers except for x = 2 and x = -2, since the expression x²-4 cannot be zero.
Therefore, the domain of f o g is all real numbers except for x = 2 and x = -2.