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The function f(x) = "max"{(1-x), (1+x), ...

The function `f(x) = "max"{(1-x), (1+x), 2}, x in (-oo, oo)` is

A

Continuous at all points

B

Differentiable at all points

C

Differentiable at all points except at `x=1 and x=-1`

D

Continuous at all points except at `x=1 and x=-1`, where it is discontinuous

Text Solution

Verified by Experts


From the graph, `y= f(x)` is non-differentiable at `x=pm 1`.
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CENGAGE PUBLICATION-GRAPHS OF ELEMENTARY FUNCTIONS -EXERCISES
  1. Draw the graph of f(x) =y= |x-1|+3|x-2|-5|x-4| and find the values of ...

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  2. Find the set of real value(s) of a for which the equation |2x+3|+2x-3|...

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  3. Draw the graph of y= 2^(((|x|+x))/(x)).

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  4. Draw the graph of y= x ^((1)/(log(e)x)).

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  5. Find the number of solutions to the equation x+log(e)x=0.

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  6. draw the graph of f(x)=x+[x], [.] denotes greatest integer function.

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  7. Given f(x) is a periodic function with period 2 and it is defined as ...

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  8. Draw the region of relation [x][y]= 6, x, y ge 0. Here [*] denotes the...

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  9. lim(xrarrc)f(x) does not exist for wher [.] represent greatest integ...

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  10. Let f(x) = ([x]+1)/({x}+1) for f: [0, (5)/(2) ) to ((1)/(2) , 3], whe...

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  11. Draw the graph of y= 2^({x}), where {*} represents the fractional part...

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  12. The area of the region containing the points (x , y) satisfying 4lt=x^...

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  13. Draw the graph of y= -sqrt(x^(2)+2)

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  14. Draw the graph of y=|x|^(1/2) for -1lt=x<1.

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  15. Draw the graph of f(x) = "sgn"(log(0.5) x).

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  16. The graph of y=f(x) is as shown in the following figure. Draw the grap...

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  17. Discuss the continuity of f(x)=(lim)(n->oo)(x^(2n)-1)/(x^(2n)+1)

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  18. An even periodic function f:R to R with period 4 is such that f(x)=...

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  19. The function f(x) = "max"{(1-x), (1+x), 2}, x in (-oo, oo) is

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  20. If f (x) = min { 1, x^2 , x^3} then

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