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Letf:RrarrR and g:RrarrR be respectively...

Let`f:RrarrR` and `g:RrarrR` be respectively given by `f(x)=|x|+1 and g(x)=x^2+1`. Define `h:RrarrR` by
`h(x)={(max {f(x),g(x)} if x le 0),(min {f(x),g(x)} if x gt 0):}`
The number of points at which `h(x)` is not differentiable is

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Verified by Experts

First we draw the graph, of `y= |x|+1 and y = x^(2) + 1`
`" "y = |x|+1 = {{:( x+1",",, x ge 0),( -x+1",",, xlt 0):}`
`y=x^(2)+1` is a parabola having vertex at (0, 1) and concave upwards
Thus, the graphs of both functions are as shown in the following figure.

From the graph, the required function is
`" "h(x) ={{:(x^(2)+1",",, x in (-oo, -1)), (-x+1",",, x in [-1, 0)), (x^(2)+1",",, x in [0, 1)), (x+1",",, x in [1, oo)):}`
which is non-different at `x=-1, 0 and 1`.
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CENGAGE PUBLICATION-GRAPHS OF ELEMENTARY FUNCTIONS -EXERCISES
  1. Letf:RrarrR and g:RrarrR be respectively given by f(x)=|x|+1 and g(x)=...

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  2. Draw the graph of y= (1)/((1//x)).

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  3. (a) Draw the graph of f(x) = ={{:(1",",, |x| ge 1), ((1)/(n^(2)) ",",,...

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  4. Sketch the regions which points satisfy |x+y| ge 2.

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  5. Sketch the region satisfying |x| lt |y|.

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  6. For a point P in the plane, let d1(P)a n dd2(P) be the distances of th...

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  7. Draw the graph of y= (x-1)/(x-2).

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  8. The following figure shows the graph of f(x) =ax^(2)+bx +c, then find ...

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  9. The entire graphs of the equation y=x^2+kx-x+9 is strictly above the x...

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  10. If x^2+2a x+a<0AAx in [1,2], the find the values of adot

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  11. Draw the graph of f(x) = x|x|.

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  12. Draw the graph of the function: Solve |(x^2)/(x-1)|lt=1 using the grap...

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

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  14. Draw the graph of y = {{:(2^(x)",",, x^(2)-2x le 0 ),( 1+3.5 x- x^(2),...

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  15. Draw the graph of f(x)= |2x-1|+ |2x-3|. Find the range of the function...

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  16. Draw the graph of f(x) =y= |x-1|+3|x-2|-5|x-4| and find the values of ...

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

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

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

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

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

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