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f(x)=sqrt(x)
g(x) = x^2+3
H(x)=sqrt x^2+3
g(x) = x^2+3
Step 1: Identify the inner function:
Looking at the expression H(x) = โ(x^2 + 3), the inner function is x^2 + 3, which is inside the square root.
Step 2: Determine the outer function:
Since the outer function takes the square root of the inner function, we can let f(x) = โx.
Step 3: Find g(x) using the inner function:
We can let g(x) = x^2 + 3.
Step 4: Verify that f ยท g = H(x):
Now, let's verify if f(x) ยท g(x) equals H(x):
f(g(x)) = f(x^2 + 3) = โ(x^2 + 3) = H(x).
Therefore, the functions f(x) = โx and g(x) = x^2 + 3 will satisfy f ยท g = H(x) = โ(x^2 + 3).