Question

Question #5cca3

Answer 1

Set the equations equal at the boundaries.

Explanation:

For the piecewise function to connected at the boundaries. the following equations must be true:

`x^-1 = ax+b; x =-1" [1]"`
`x^-1 = ax+b; x = 1/2" [2]"`

Substitute the values of x

`-1 = -a+b" [1.1]"`
`2 = 1/2a+b"[2.1]"`

Subtract equation [1.1] from equation [2.1]:

`3 = 3/2a`

a = 2

Use equation [1.1] to find the value of b:

`-1 = -2+b`

`b = 1`

Here is a graph of the piecewise function

`y = { (x^-1; x < -1),( 2x+1 ; -1 <= x <= 1/2),( x^-1 ; x > 1/2):}`