Question

Suppose that the function g is defined, for all real numbers, as follows.-3if xs-2g(x) = (x - 1)2 - 1 if -2

Answer 1

g(-4) = -3

g(-2) = -3

g(-1) = 3

What we have in this question is a piece-wise function

The function takes on certain values at cerain ranges

For example, if the given value of x that we want to evaluate is less than or equal to -2, then the value of the function is -3

Secondly, in cases where the values of x is between -2 and 1, we will use the second equation (meaning where we have x as -1 and 0)

Then lastly, when x is greater than or equal to 1 , then we will use the third function

So we have to understand the range where we have the value to be calculated so as to know which of the equation in the piece-wise function to use.

Let us proceed;

a) g(-4)

Since -4 is less than -2, what we will have as answer here is that g(x) = -3

b) g(-2)

Since -2 is equal to -2, it falls in the first range so the value of g(x) here is -3

c) g (-1)

This falls in the second range , so we are going to use the second equation;

`\begin{gathered} g(x)=(x-1)^2\text{ -1 } \\ \\ \text{where x = -1} \\ \\ g(-1)=(-1-1)^2-1 \\ \\ g(-1)=(-2)^2-1\text{ = 4-1 = }3 \end{gathered}`