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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-GRAPHS OF ELEMENTARY FUNCTIONS -Exercise
  1. Draw the graph of y= |x-1|+3|x-2|-5|x-4| and find the values of lamda ...

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

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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. Find tha area of the region containing the points (x, y) satisfying 4...

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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) from -1 le x le 1.

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

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  16. Graph of y= f(x) is given as shown in the following figure. Draw the...

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  17. Draw the graph of the function y= f(x) = lim(n to oo) (x^(2n)-1)/(x^(...

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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. Check the differentiability if f(x) = min. {1, x^(2), x^(3)}.

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