# Function Composition

Function composition is a fundamental concept in mathematics and computer science that involves combining two or more functions to create a new function. This process allows for the sequential application of functions, where the output of one function serves as the input for another. By composing functions, complex operations can be broken down into simpler, more manageable components, facilitating clearer understanding and more efficient problem-solving. Understanding function composition is essential in various fields, including calculus, linear algebra, and programming, where it forms the basis for constructing sophisticated algorithms and modeling complex systems.

Questions

- How do you find the inverse of #p(x)=x^3-3x^2+3x-1#?
- How do you find the inverse of #y=log(x+2)#?
- Let #s(x) = x ^2 + 2x + 3x# and #t(x) = sqrt(x+4), how do you find sot(6)?
- How do you find the inverse of #2x-2# and is it a function?
- How do you find the compositions given #f(x) = |x - 2#|, #g(x) = sqrtx#?
- How do you find the inverse of #f(x) =2x-5# and is it a function?
- How do you find the inverse of #f(x)= x/(x-9)#?
- How do you find the inverse of #f(x)=2x+3#?
- How do you find the inverse of #y =1/logx#?
- How do you use composition of functions to show that #f(x)=(2+x)/x# and #f^-1(x) = 2/(x-1)# are inverses?
- How do you find the inverse of #y=(4x+2)/(x-7)#?
- How do you find #h(x)=f(x)-g(x)# given #f(x)=6-x# and #g(x)=(x+1)^2-2#?
- How do you find the inverse of #f(x)=3^(x-1)-2#?
- How do you find the inverse of #y=log_6 x#?
- Let #u(x)=2x-1# and #w(x)=x^2#, how do you find u(w(-4)) and w(u(-4))?
- How do you find 2p(a) + p(a - 1) if #p(x) = x^2 + x#?
- How do you find the inverse of # f(x)=log(x+15)#?
- How do you find the inverse of #y=ln(x+2)#?
- How do you use the horizontal line test to determine whether the function #f(x)=1/8(x+2)^2-1# is one to one?
- Given the functions #F(x)=x+4# and #G(x)=2x^2+4# what is f(g(x))?