Consider the sets $X=\{0, 3, -1\}, Y=\{3, 7, 9\}, Z=\{\text{black}, \text{white}\}$.

Question

Consider the sets $X=\{0, 3, -1\}, Y=\{3, 7, 9\}, Z=\{\text{black}, \text{white}\}$.

Let $f: X \to Y$ be the function defined by $f(0)=7$, $f(3)=9$, $f(-1)=7$. Let $g: Y \to Z$ be the function defined by $g(3)=\text{black}$, $g(7)=\text{black}$ and $g(9)=\text{white}$. Describe the composite function $h=g \circ f : X \to Z$ explicitly.

So far I have:

1. $g \circ f(0) = g (7) = \text{black}$

2. $g \circ f(3) = g(9) = \text{white}$

3. $g \circ f(-1) = g(7) = \text{black}$

Is this enough to answer the question? And what does it mean by describe "explicitly"? Thanks.

Answer 1

As $h=g \circ f : X \to Z$ you only need to define for the elements of $X$. You did. I'm assuming "explicitly" means so that every possible value is adequately defined but I'm not $100\%$ sure.

You listed $h(x)$ for every possible value of $X$ so you did fine.

Although your title states $X = \{0, 3, 1\}$ and your problem states $-1$ rather than $1$.