If:
f(x)= radical x
g(x)= x^2+1
What is the domain of f o g?
I don't really understand how to answer this question.
f{g(x)} = sqrt(x^2+1)
The domain is all numbers greater than 1, unless you also allow the negative square root as one of two radical x values. In that case you can also have
f{g(x)} numbers less than -1.
The formula for f{g(x)} is correct, but I got the domain and range mixed up.
x can have any real value, so the domain of f{g(x)} extends from -infinity to infinity.
To find the domain of the composition function f o g, we need to consider two things:
1. The domain of g(x): Since g(x) is a polynomial function, its domain is the set of all real numbers, (-∞, ∞).
2. The domain of f(y): The domain of f(y) is determined by the allowable values of y when we substitute f(y) into the composition f o g. In this case, y represents the output of g(x), so it can take any real value.
Combining both domains, we conclude that the domain of f o g is (-∞, ∞), just like the domain of g(x).
In summary, the domain of f o g is (-∞, ∞), meaning that any real number can be input into the composition function.