Question

Please help asap!
i need the answer for f(-2), f(-1), f(5)

Answer 1

`\sf\\Given:\\f(x)=3\ \ \ \{\textsf{if }x\ < -2\}\\f(x)=(x+1)^2-3\ \ \ \{\textsf{if }-2\le x < 2\}\\f(x)=-(1)/(2)x-1\ \ \ \{\textsf{if }x\ge2\}`

`\sf\\\textsf{In case of f(-2), }x=-2.\\\textsf{Here, }-2\le x < 2. \textsf{So we use the second case.}\\f(-2)=(-2+1)^2-3=1^2-3=-2`

`\sf\\\textsf{In case of f(-1), }x=-1.\\\textsf{Here }-2\le x < 2, \textsf{So we use the second case.}\\\therefore\ f(-1)=(-1+1)^2-3=0-3=-3`

`\sf\\\textsf{In f(5), }x=5\ i.e.\ x\ge2. \textsf{So we use the third value of f(x).}\\f(5)=-((1)/(2))5-1=-(7)/(2)`