1. ## composition of functions

Hey I have no idea how to do this question...can you point me in the right way please

Consider the following functions:
f(x) = x + 1, g(x) = x − 1, h(x) = 2x, m(x) = 4x, n(x) = x^2, p(x) = √x, and q(x) = 2x + 1.
Use composition of functions and one or more of f , g, h, m, n, p and q to define two new functions: y(x) = x^2 − 2x + 1 and z(x) = 4x^2

Thanks for any help

Hey I have no idea how to do this question...can you point me in the right way please

Consider the following functions:
f(x) = x + 1, g(x) = x − 1, h(x) = 2x, m(x) = 4x, n(x) = x^2, p(x) = √x, and q(x) = 2x + 1.
Use composition of functions and one or more of f , g, h, m, n, p and q to define two new functions: y(x) = x^2 − 2x + 1 and z(x) = 4x^2

Thanks for any help
For example $\displaystyle f(g(x))=(x-1)^2=x^2-2x+1$

Hey I have no idea how to do this question...can you point me in the right way please

Consider the following functions:
f(x) = x + 1, g(x) = x − 1, h(x) = 2x, m(x) = 4x, n(x) = x^2, p(x) = √x, and q(x) = 2x + 1.
Use composition of functions and one or more of f , g, h, m, n, p and q to define two new functions: y(x) = x^2 − 2x + 1 and z(x) = 4x^2

Thanks for any help
Originally Posted by Mathstud28
For example $\displaystyle f(g(x))=(x-1)^2=x^2-2x+1$
@Mathstud 28: Where did you get that?
$\displaystyle f(g(x)) = f(x - 1) = (x - 1) + 1 = x$

Now
$\displaystyle n(g(x)) = n(x - 1) = (x - 1)^2 = x^2 - 2x + 1$

For the second problem, I would like to draw your attention to m(x) and n(x). Can you use these to form $\displaystyle 4x^2$?

-Dan