Question

Suppose that the function g is defined, for all real numbers, as follows g(x)=[-1/4x+1 If x<-2} -(x+1)^ 2+1 If -2 ≤ x ≤ 2 2 If x >2 Find g (-2), g(-1) ,and g(4) plz help me ...!!!

Answer 1

(a)0

(b)1

(c)2

Explanation:

The function g is defined as follows:

`g=\left\{\begin{array}{ccc}-(1)/(4)x+1, &x<-2 \\-(x+1)^2+1, &-2\leq x\leq2\\2,&x>2\end{array}\right\\`

`(a)g(x)=-(x+1)^2+1, -2\leq -2\leq2\\g(-2)=-(-2+1)^2+1=0\\`

`(b)g(x)=-(x+1)^2+1, -2\leq -1\leq2\\g(-1)=-(-1+1)^2+1=1\\`

`(c)g(x)=2, x>2\\Therefore, g(4)=2`