Question

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

Answer 1

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

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`