6) Find the composition of the function.f(x) = x^1/2 and g(x) = 1/x Find f(g(x)).
To find the composition of the functions f(x) = x^(1/2) and g(x) = 1/x, we need to substitute g(x) into f(x)
To find the composition of the functions f(x) = x^(1/2) and g(x) = 1/x, we need to substitute g(x) into f(x).
The composition of two functions is written as (f o g)(x), which is read as “f composed with g of x”. In this case, we want to find f(g(x)), which means we substitute g(x) into f(x).
So, let’s substitute g(x) into f(x):
f(g(x)) = f(1/x)
Now, replace x in f(x) with 1/x:
f(g(x)) = (1/x)^(1/2)
To simplify this, remember that raising a fraction to an exponent means raising the numerator and denominator separately:
f(g(x)) = (1^(1/2))/(x^(1/2))
The square root of 1 is simply 1:
f(g(x)) = 1/(x^(1/2))
And if we rewrite x^(1/2) as the square root of x, the final result is:
f(g(x)) = 1/√(x)
Therefore, the composition of the functions f(x) = x^(1/2) and g(x) = 1/x is f(g(x)) = 1/√(x).
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