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If f(x)={a x^2+b ,0lt=x<1 4,x=1x+3,1<xg...

If `f(x)={a x^2+b ,0lt=x<1 4,x=1x+3,1

A

(2,2)

B

(3,1)

C

(4,0)

D

(5,12)

Text Solution

Verified by Experts

The correct Answer is:
D
We observe that `underset(xto1^(+))lim f(x)=f(1),` So, f(x) is right continous at x=1. Thus f(x) will not be continous at x=1 only if
`i.e. underset(x to 1^(+))lim f(x) ne f(1)`
`i.e. underset(x to1)lim (ax^(2)+b) ne 4 or, a+b=4`
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OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. If f(x)={a x^2+b ,0lt=x<1 4,x=1x+3,1<xgeq2 then the value of (a , b) ...

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  2. The function f(x) = (4-x^(2))/(4x-x^(3)) is discontinuous at

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  3. Let f(x)=|x| and g(x)=|x^3| , then (a).f(x) and g(x) both are continuo...

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  4. The function f(x)=sin^(-1)(cosx) is discontinuous at x=0 (b) continuou...

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  5. The set of points where the function f(x)=x|x| is differentiable is...

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  6. On the interval I = [-2, 2], if the function f(x) = {{:((x+1)e^(-((1)/...

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  7. If f(x)={{:(,(|x+2|)/(tan^(-1)(x+2)),x ne -2),(,2, x=-2):}, then f(x) ...

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  8. Let f(x)=(x+|x|)|x| . Then, for all x f is continuous

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  9. The set of all points where the function f(x)=sqrt(1-e^(-x^2)) is di...

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  10. The function f(x)=e^(-|x|) is continuous everywhere but not differe...

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  11. The function f(x)=[cos x] is

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  12. If f(x)=sqrt(1-sqrt(1-x^2)) , then f(x) is (a) continuous on [-1, 1] ...

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  13. If f(x) = sin ^(-1)((2x)/(1 + x^(2))) then f (x) is differentiable in ...

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  14. about to only mathematics

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  15. If f(x)=|x-a|varphi(x), where varphi(x) is continuous function, then f...

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  16. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)+. . . . +(x^2)/((1+x^2)^n)...

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  17. If f(x)= | log10x| then at x=1.

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  18. If f(x)=|log(e) x|,then

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  19. If f(x)=|log(e)|x||," then "f'(x) equals

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  20. Let f(x)={1/(|x|)\ \ \ \ \ for\ |x|geq1a x^2+b\ \ \ \ \ \ \ \ for\ |x|...

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  21. Let h(x)="min "{x,x^(2)} for every real number of x. Then, which one o...

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