Algebra

Functions

Composition of Functions

         

Given two functions:

f(x)=x+3f(x)=x+3

g(x)=x2g(x)=\dfrac{x}{2}

Find the value of g(f(5))g(f(5)).

For the two functions f(x)=x2+5x,g(x)=x+22,f(x)=x^2+5x, \, g(x)=x+22, what is the value of (gf)(9)?(g \circ f)(9)?

Details and assumptions

(gf)(x) (g \circ f)(x) is the composition of gg and ff, defined by (gf)(x)=g(f(x))(g \circ f)(x)= g(f(x)).

Let ff be a function such that (ff)(x)=x2(f \circ f)(x) = x^2

What is the value of f(f(f(f(f(f(2))))))?f(f(f(f(f(f(2))))))?

Consider the two functions f(x)=6x5,g(x)={x+4 if x1,17 if x<1.f(x)=6x-5, g(x)=\begin{cases} -x+4 & \text{ if } x \geq 1, \\ 17 & \text{ if } x<1. \end{cases} What is the value of (fg)(2)+(gf)(0)(f \circ g)(2)+(g \circ f)(0)?

Details and assumptions

(gf)(x) (g \circ f)(x) is the composition of gg and ff, defined by (gf)(x)=g(f(x))(g \circ f)(x)= g(f(x)).

f:RR f: \mathbb{R} \rightarrow \mathbb{R} is a function satisfying f(2x+1)=4x2+4x f( 2x+1) = 4x^2 + 4x. What is the value of f(16)f(16)?

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