SOLUTION: What does it mean to "find the domain and range of the composition f of g? and to write the answer in "set notation" ??? Thank you

Question 455322: What does it mean to "find the domain and range of the composition f of g? and to write the answer in "set notation" ??? Thank you
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
What does it mean to "find the domain and range of the composition f of g? and to write the answer in "set notation" ???
---
A function is a machine. You feed it "x" and
it gives you f(x).
Now, if you feed f(x) to another machine, g,
you will get g[f(x)]
----
That is what composition is. It's two machines
operating one after another.
---
Example:
f(x) = x+3
g(x) = 2x
---
fog(x) = f[g(x)] = f[2x] = 2x+3
---
OR
gof(x) = g[f(x)] = g[x+3] = 2(x+3) = 2x+6
=================================
If an answer happens to be x = 2, or x = 3
the set notation would look like {x | x = 2 or x = 3}
=======================================================
Cheers,
Stan H.
RELATED QUESTIONS
For f(x)=x^2 and g(x)=sqr(2x), find the following. the domain of g. My answer x≥0 (answered by Gogonati)

find the domain and range of each function. write your answer in interval notation. F(x)= (answered by lwsshak3)

Find the domain and range of \sqrt{x} + 9 Write the answer in interval... (answered by lwsshak3)

For the real-valued functions f(x) =4x+5 and g(x) = √x-4 find the composition... (answered by Boreal)

f(x)=x^2-2x-24 a - Determine the vertex? b - Does the graph open up or down? c -... (answered by MathLover1)

If f(x)=1/√x and g(x)=x^2-10x+25, demonstrate how to find the composition. Be sure to... (answered by ikleyn)

y=f(x) find the domain and range of f and use interval notation (answered by MathLover1)

What is the domain and range in set notationa and interval notation of... (answered by nerdybill)

find the domain of f and write it in interval notation. f(x)=... (answered by MathLover1)