Exercise 1.1.4

Question

The graphs of $f$ and $g$ are given.
    \begin{enumerate}[label=(\alph*)]
        \item State the values of $f(-4)$ and $g(3)$.
        \item Which is larger, $f(-3)$ or $g(-3)$?
        \item For what values of $x$ is $f(x)=g(x)?$
        \item On what interval(s) is $f(x) \leq g(x)$ ?
        \item State the solution of the equation $f(x) = -1.$
        \item On what interval(s) is $g$ decreasing?
        \item State the domain and the range of $f$.
        \item State the domain and the range of $g.$
    \end{enumerate}

Khagan Gulusoy · Accepted Answer

\begin{enumerate}[label=(\alph*)]
    \item $f(-4)=-2;\quad g(3) = 4.$
    \item $f(-3)=-1; \ g(-3)=2 \implies g(-3)>f(-3).$ 
    \item To find for what values of $x$ is $f(x)=g(x),$ we must first find the intersection point between $f$ and $g$. These points are $(-2, \ 1)$ and $(2, \ 2).$ Since we need to find x-coordinates, the answer is $-2; \ 2.$
    \item For all $x$ in the interval $[-4, \ -2]\cup [2, \ 3]$, we have $f(x)\leq g(x).$ Note that on $(3, \ 4]$ function $g$ is not defined and $f(x)\leq g(x)$ does not make sense.
    \item $f(x)=-1\implies x\in \{ -3, \ 4\}.$
    \item $[-4, \ 0].$
    \item The domain of $f$ is $[-4, \ 4];$ the range is $[-2, \ 3].$
    \item The domain of $g$ is $[-4, \ 3];$ the range is $[0.5,\ 4].$    
\end{enumerate}

Exercise 1.1.4

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Exercise 1.1.4

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