If f(x)=x^2-2 and g(x)=1/(3x) (x does not equal 0), find (f+g)(x) and f(fxg)(-2)
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To find (f+g)(x), we need to add the functions f(x) and g(x).
Step 1: Evaluate f(x) = x^2 - 2 and g(x) = 1/(3x).
Step 2: Add the two functions together:
(f+g)(x) = f(x) + g(x)
= (x^2 - 2) + (1/(3x))
= x^2 - 2 + (1/(3x))
Please note that the function (f+g)(x) will be defined as long as the denominator in g(x) is not zero.
Now let's find f(fxg)(-2). Here, we need to substitute -2 for x and simplify the expression.
Step 1: Evaluate f(x) = x^2 - 2.
f(-2) = (-2)^2 - 2
= 4 - 2
= 2
Step 2: Evaluate g(x) = 1/(3x).
g(-2) = 1/(3*(-2))
= 1/(-6)
= -1/6
Step 3: Substitute the results from Step 1 and Step 2 into the expression f(fxg)(-2) and simplify.
f(fxg)(-2) = f(2*(-1/6))
= f(-1/3)
= (-1/3)^2 - 2
= 1/9 - 2
= -17/9
Therefore, f(fxg)(-2) simplifies to -17/9.