7) Find the composition of the function.f(x) = x^1/2 and g(x) = 1/x Find g(f(x)).
To find the composition g(f(x)), we first substitute f(x) into the function g(x)
To find the composition g(f(x)), we first substitute f(x) into the function g(x).
Let’s start with f(x) = x^(1/2).
Substituting f(x) into g(x) gives us:
g(f(x)) = g(x^(1/2))
Now let’s substitute this expression into the function g(x) = 1/x:
g(f(x)) = 1/(x^(1/2))
To simplify this expression, we can rewrite the denominator as a fractional exponent:
g(f(x)) = 1/(x^(1/2)) = 1/(√x)
So, the composition of the functions f(x) = x^(1/2) and g(x) = 1/x is given by g(f(x)) = 1/(√x).
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Simplifying the composition of functions f(x) = x^(1/2) and g(x) = 1/x into f(g(x)) = 1/√(x)
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