CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Let $$f:R\rightarrow R$$ be defined by $$f\left( x \right) =2x+\left| x \right|$$ Then prove that $$f\left( 2x \right) +f\left( -x \right) -f\left( x \right) =2\left| x \right|$$.


Solution

$$f\left(x\right)=2x+\left|x\right|$$

$$f\left(2x\right)=4x+\left|2x\right|=4x+2\left|x\right|$$

$$f\left(-x\right)=-2x+\left|-x\right|=-2x+\left|x\right|$$

Now, $$ f\left(2x\right)+ f\left(-x\right)- f\left(x\right)=4x+2\left|x\right|-2x+\left|x\right|-2x-\left|x\right|$$

$$=2\left|x\right|$$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image