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If f(x) be continuous function and g(x...

If f(x) be continuous function and g(x) be discontinuous, then

A

`f(x)+g(x)` must be continuous

B

`f(x)+g(x)` must be discontinuous

C

`f(x)=g(x)` for all x

D

Can't say

Text Solution

Verified by Experts

The correct Answer is:
B
If possible, suppose that f(x) + g(x) is continuous.
Now, `g(x)=[f(x)+g(x)] -f(x)`
Since, difference of two continuous functions is continuous, therefore g(x) is continuous, which is a contradiction.
Hence, f(x) + g(x) must be discontinuous.
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-CONTINUITY-EXERCISE 2 (MISCELLANEOUS PROBLEMS)
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  2. The function y =3sqrt(x)-|x-1| is continuous at

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  3. lim(n to oo) (1^(2)+2^(2)+3^(2)+…+n^(2))/(n^(3)) is equal to

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  4. If 0 lt a lt b, " then " lim(n to oo) (a^(n)+b^(n))/(a^(n)-b^(n))

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  5. lim(x to 0)((1+x)^(8)-1)/((1+x)^(2)-1) is equal to

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  6. If the function f(x) satisfies lim(x to 1) (f(x)-2)/(x^(2)-1)=pi, then...

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  7. lim(x to0) (-1)^([x]) where [.] denotes the greatest function is equal...

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  8. If lim(x to 1) (ax^(2)+bx+c)/((x-1)^(2))=2, then (a, b, c) is

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  9. lim(m to oo)("cos"(x)/(m))^(m) is equal to

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  10. The value of lim( x to 3) (x^(5)-3^(5))/(x^(8)-3^(8)) is equal to

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  11. lim(x to 0) ((1-cos 2x)(3+cosx))/(x tan 4x) is equal to

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  12. At x=3, f(x) ={(x^(5)-243",", "if " x ne 3),(x^(3)-27",", "if " x=3):}...

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  13. The value of f(0), if f(x)=(x tan 2x)/(sin3x sin5x) is continuous at ...

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  14. f(x)={((5^(cosx)-1)/((pi)/(2)-x)",", x ne (pi)/(2)), (log 5"," , x =(p...

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  15. If f(x)={((sqrt(1+px)-sqrt(1-px))/(x) ",", -1 le x lt 0),((2x+1)/(x-2...

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  16. The function f(x)=(x^3+x^2-16 x+20)/(x-2) is not defined for x=2. In o...

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  17. In order that the function f(x)=(x+1)^(cotx) is continuous at x = 0, t...

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  18. if f(x) is continuous and f(9/2)=2/9 then the value if lim(x->0)f((1-c...

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  19. If f(x)={(ax+1",", x le (pi)/(2)),(sinx+b",", x gt (pi)/(2)):} is cont...

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  20. If f(x)={((1+2x)^(1//x)",","for " x ne 0),(e^(2)",", "for " x =0):}, t...

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