Question

Suppose that the function H is defined, for all real numbers, as followers

Answer 1

SOLUTION

From the question, we have that

$\begin{gathered} h(x)=-3 \\ \text{if }x\le-2 \\ \end{gathered}$

so for

$\begin{gathered} h(-4) \\ x\text{ here is -4 and -4 is less than -2, so it satisfies that equation above} \\ \end{gathered}$

Hence

$h(-4)=-3$

Also for

$\begin{gathered} h(-2) \\ x\text{ here is -2 and -2 is equal to -2, so it satisfies the equation} \end{gathered}$

Hence

$h(-2)=-3$

Finally, we have that

$\begin{gathered} h(x)=-(x+1)^2+2 \\ \text{if -2}So [tex]\begin{gathered} h(1) \\ x\text{ here is 1 and 1 is greater than -2, but less than 2} \\ so\text{ it satisfies the equation.} \end{gathered}$

Hence we have that

$\begin{gathered} h(x)=-(x+1)^2+2 \\ h(1)=-(1+1)^2+2 \\ h(1)=-(2)^2+2 \\ =-4+2 \\ -2 \end{gathered}$

Hence

$h(1)=-2$