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We say an equation f(x)=g(x) is consiste...

We say an equation `f(x)=g(x)` is consistent, if the curves `y=f(x) and y=g(x)` touch or intersect at atleast one point. If the curves `y=f(x) and y=g(x)` do not intersect or touch, then the equation `f(x)=g(x)` is said to be inconsistent i.e. has no solution.
The equation `cosx+cos^(-1)x=sinx+sin^(-1)x` is

A

consistent and has infinite number of solutions

B

consistent and has finite number of solutions

C

inconsistent

D

None of the above

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • We say an equation f(x)=g(x) is consistent, if the curves y=f(x) and y=g(x) touch or intersect at atleast one point. If the curves y=f(x) and y=g(x) do not intersect or touch, then the equation f(x)=g(x) is said to be inconsistent i.e. has no solution. The equation sinx=x^(2)+x+1 is

    A
    consistent and has infinite number of solutions
    B
    consistent and has finite number of solutions
    C
    inconsistent
    D
    None of the above

  • We say an equation f(x)=g(x) is consistent, if the curves y=f(x) and y=g(x) touch or intersect at atleast one point. If the curves y=f(x) and y=g(x) do not intersect or touch, then the equation f(x)=g(x) is said to be inconsistent i.e. has no solution. Among the following equations, which is consistent in (0, pi//2) ?

    A
    `sinx+x^(2)=0`
    B
    `cosx=x`
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    `tanx=x`
    D
    All of these

  • If : f(x)=x^2 and g(x)=2^x, then, the solution set of the equation (f@g)(x)=(g@f)(x) is

    A
    R
    B
    `{0}`
    C
    `{0,2}`
    D
    `R^+`

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