Home
Class 12
MATHS
Draw a graph of the function y = [x] +|...

Draw a graph of the function `y = [x] +|1 - x|,-1 leq x leq 3`. Determine the points if any, where this function is not differentiable.

Text Solution

Verified by Experts

The correct Answer is:
`{0, 1, 2)`
`y=[x] + |1-x|, -1 le x le 3`
`rArr" " y = {{:(-1+1-x", " -1 le x lt 0),(0+1-x", " 0 le xlt1),(1+x-1", " 1 le x lt 2),(2+x-1", " 2 le xle 3):}`
`rArr" "y={{:(-x", " -1le x lt0),(1-x", " 0le xlt1),(+x", " 1le xlt 2),(x+1", " 2le xlt3):}`
which could be shown as,

Clearly, from above figure, y is not continuous and not differentiable at `x = {0, 1, 2}`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Draw the graph of the function f(x)=x^2

Draw the graph of the function f(x) =x^x .

Draw the graph of the function: f(x)=log|x|

Draw the graph of the function: f(x)=||x-2|-3|

Draw the graph of the function: |f(x)|=tanx

Draw the graph of the function f(x) =x-sqrt(x) .

Draw the graph of the function f(x) = (1+1/x)^(2)

Draw the graph of the function: f(x)=|x^2-3|x|+2|

Draw the graph of the function f(x)= x- |x-x^(2)|, -1 le x le 1 and find the points of non-differentiability.

Draw the graph of the function: f(x)=-|x-1|^(1/2)