Composition of Functions

[chrisdchase]

I am having trouble understanding composition of functions. The problem that I am working on is, "Find the functions of, (f o f), (g o f), (f o f),(g o g) & their domains. f(x)= x² g(x)= sqrt of x-3. I have the domains of f(x)= (-infinity, infinity) & g(x)= [0, infinity). I have calculated (f o g) = f(g(sqrt x-3)). This equals f(sqrt x-3). I am guessing that the definition would = (sqrt x-3)^{2 ? I am very confused and hope someone could help point me into the right direction. Thank you.}

 

[mathmari]

I am having trouble understanding composition of functions. The problem that I am working on is, "Find the functions of, (f o f), (g o f), (f o f),(g o g) & their domains. f(x)= x² g(x)= sqrt of x-3. I have the domains of f(x)= (-infinity, infinity) & g(x)= [0, infinity). I have calculated (f o g) = f(g(sqrt x-3)). This equals f(sqrt x-3). I am guessing that the definition would = (sqrt x-3)^{2 ? I am very confused and hope someone could help point me into the right direction. Thank you.}

^{\(\displaystyle (f o g)(x)=f(g(x))=f(\sqrt{x-3})=(\sqrt{x-3})^2=x-3 \)}

 

[srmichael]

I am having trouble understanding composition of functions. The problem that I am working on is, "Find the functions of, (f o f), (g o f), (f o f),(g o g) & their domains. f(x)= x² g(x)= sqrt of x-3. I have the domains of f(x)= (-infinity, infinity) & g(x)= [0, infinity). I have calculated (f o g) = f(g(sqrt x-3)). This equals f(sqrt x-3). I am guessing that the definition would = (sqrt x-3)^{2 ? I am very confused and hope someone could help point me into the right direction. Thank you.}

<sup>First, the domain of g(x) is [3,∞), not [0,∞)

When doing composition of functions you are substituting in for the variable in the function another function. Thus (f o f) means f(f(x)) so you would substitute in the function f(x) into the function f(x) for x. Just as you would know that f(3) = 3² = 9, instead of a number like 3 it is now just another function.

(f o f) = f(f(x)) = f(x²) = (x²)² = x^4.

See if you can do (g o f) and (g o g) as mathmari already provided you with (f o g).</sup>