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Show that the function f defined by f(x)...

Show that the function `f` defined by `f(x)=|1-x+|x||` is everywhere continuous.

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To show that the function \( f \) defined by \( f(x) = |1 - x + |x|| \) is everywhere continuous, we will analyze the function by breaking it down into different cases based on the values of \( x \). ### Step 1: Understanding the function The function involves absolute values, so we need to consider different cases for \( x \): 1. When \( x \geq 0 \) 2. When \( x < 0 \) ### Step 2: Case 1: \( x \geq 0 \) ...
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RD SHARMA-CONTINUITY-Solved Examples And Exercises
  1. Discuss the continuity of the function f(x)={(|x|)/x\ \ \ ,\ \ \ if...

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  2. Discuss the continuity of the function f(x) given by f(x)={2x-1,ifx<0...

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  3. Show that the function f defined by f(x)=|1-x+|x|| is everywhere co...

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  4. Prove that f(x)=sqrt(|x|-x) is continuous for all xgeq0 .

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  5. Given f(x)=1/(x-1) . Find the points of discontinuity of the compos...

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  6. Determine the value of the constant k so that the function f(x)={k ...

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  7. Determine the value of the constant m so that the function f(x)={m(...

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  8. If f(x)={1\ \ \ ,\ \ \ if\ xlt=3a x+b\ \ \ ,\ \ \ if\ 3<x<5 7\ \ \ ,\ ...

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  9. Prove that the function f(x)={(sinx)/x\ \ \ ,\ \ \ x<0x+1\ \ \ ,\ \...

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  10. Discuss the continuity of the function fx)={x/(|x|)\ \ \ ,\ \ \ x!=0...

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  11. Find the points of discontinuity, if any, of the following function...

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  12. Find the points of discontinuity, if any, of the following function...

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  13. Find the points of discontinuity, if any, of the following function...

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  14. Find the points of discontinuity, if any, of the following function...

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  15. Find the points of discontinuity, if any, of the following function...

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  16. Find the points of discontinuity, if any, of the following function...

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  17. Find the points of discontinuity, if any, of the following function...

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  18. Find the points of discontinuity, if any, of the following function...

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  19. Find the points of discontinuity, if any, of the following function...

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  20. Find the points of discontinuity, if any, of the following function...

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