Question

1.9 exit ticket: (complete the questions)

1. in your own words, what does (f ∘ g)(x) mean?
2. let f(x)=x - 2 and g(x)=3x. find (f ∘ g)(-1).

Explanation:

Step1: Define function - composition

$(f\circ g)(x)$ means applying function $g$ to $x$ first and then applying function $f$ to the result of $g(x)$.

Step2: Find $g(-1)$

Given $g(x)=3x$, substitute $x = - 1$ into $g(x)$. So $g(-1)=3\times(-1)=-3$.

Step3: Find $(f\circ g)(-1)$

Since $(f\circ g)(-1)=f(g(-1))$, and $g(-1)=-3$, substitute $x=-3$ into $f(x)$. Given $f(x)=x - 2$, then $f(-3)=-3-2=-5$.

Answer:

-5