Help with domain question with g(f(x))

Thread starter mesa
Start date Sep 11, 2012
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Domain

In summary, the formula for g(f(x)) is g(f(x)) = g(f(x)). To find the domain of g(f(x)), first determine the domain of f(x) and then plug these values into g. The domain of g(f(x)) can be larger than the domain of f(x) if g introduces new values. To graph g(f(x)), first graph f(x) and then apply g to each point. The difference between g(f(x)) and f(g(x)) is the order of function application, resulting in different domains and outputs.

Sep 11, 2012

mesa

Gold Member

Homework Statement

If f(x)=√x and g(x)=√(x^2+1) what is the domain of g(f(x))?

The Attempt at a Solution

I cam up with (-∞,+∞) since the square root of a square is always positive, am I missing something here?

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Sep 11, 2012

mesa

Gold Member

Nevermind, just saw it lol

FAQ: Help with domain question with g(f(x))

What is the formula for g(f(x))?

The formula for g(f(x)) is g(f(x)) = g(f(x)). The function g is applied to the output of the function f.

How do I find the domain of g(f(x))?

To find the domain of g(f(x)), first determine the domain of f(x). Then, plug in the values from the domain of f(x) into the function g. The resulting values will be the domain of g(f(x)).

Can the domain of g(f(x)) be larger than the domain of f(x)?

Yes, the domain of g(f(x)) can be larger than the domain of f(x). This can happen when the function g introduces new values that were not originally in the domain of f(x).

How can I graph g(f(x))?

To graph g(f(x)), first graph f(x) and then apply the function g to each point on the graph of f(x). This will give you the graph of g(f(x)).

What is the difference between g(f(x)) and f(g(x))?

The difference between g(f(x)) and f(g(x)) is the order in which the functions are applied. In g(f(x)), the function f is applied first and then the function g is applied to the output. In f(g(x)), the function g is applied first and then the function f is applied to the output. This can result in different domains and outputs for each function composition.