What is the range of the function G(x)=∣x+1∣−∣x−1∣?Express your answer in interval notation.
Solution — click to reveal
We have G(x)=⎩⎨⎧−(x+1)+(x−1)(x+1)+(x−1)(x+1)−(x−1)if x<−1if −1≤x<1if x≥1.Simplifying, we have G(x)=⎩⎨⎧−22x2if x<−1if −1≤x<1if x≥1.Therefore, the range of G(x) is [−2,2].