F(x)=1/x-2 g(x)= under root x find fg
fg(x) is equal to f(g(x)). So first we substitute g(x) into f(x) to get:
f(g(x)) = 1/g(x) - 2
Since g(x) is equal to the square root of x, we substitute that in:
f(g(x)) = 1/sqrt(x) - 2
Therefore, fg(x) = 1/sqrt(x) - 2.
To find fg, we need to substitute g(x) into f(x):
f(g(x)) = f(√x)
Now, substitute g(x) = √x into f(x):
f(√x) = 1/(√x) - 2
To simplify further, we can rationalize the denominator by multiplying the numerator and denominator by √x:
f(√x) = (1/(√x) - 2) * (√x)/(√x)
Applying the distributive property:
f(√x) = (√x - 2√x)/(√x)
Combining like terms in the numerator:
f(√x) = -√x/(√x)
Simplifying the fraction:
f(√x) = -1
Therefore, fg = -1.
To find the composition fg(x), you need to substitute g(x) into f(x). This means replacing each instance of x in f(x) with g(x).
Given:
f(x) = 1/(x - 2)
g(x) = √x
Replacing x in f(x) with g(x), we get:
f(g(x)) = 1/(g(x) - 2)
Substituting g(x) = √x:
f(g(x)) = 1/(√x - 2)
Therefore, fg(x) = 1/(√x - 2).