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Consider f: R^+ rarr [4, oo] given by f(...

Consider `f: R^+ rarr [4, oo]` given by `f(x)=x^2+4.` Show that `f` is invertible with the inverse `(f^(-1))` of `f` given by `f^(-1)\ (y)=sqrt(y-4)` , where `R^+` is the set of all non-negative real numbers.

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. If vec a= hat i+ hat j+ hat k ,\ \ vec b=4 hat i-\ 2 hat j+3 hat k a...

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  2. Prove, using properties of determinants: |[y+k, y, y],[ y, y+k, y],[...

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  3. Consider f: R^+ rarr [4, oo] given by f(x)=x^2+4. Show that f is inver...

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  4. What are the direction cosines of a line, which makes equal angles ...

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  5. Evaluate: int(dx)/(x(x^5+3))

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  6. Find the value of k so that the function f defined by f(x)={(kcosx)/(...

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  7. Prove that : tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot

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  8. Find the vector and cartesian equations of the line passing through...

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  9. Evaluate: |(cos15^0,sin15^0),(sin75^0,cos75^0)|

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  10. What is the principal value of cos^(-1)cos((2pi)/3)+sin^(-1)sin((2p...

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  11. Let A = {1, 2, 3}, B = {4, 5, 6, 7}and let f = {(1, 4), (2, 5), (3, 6)...

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  12. Evaluate: int(dx)/(sqrt(1-x^2))

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  13. Evaluate: int(a x+b)^3dx

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  14. If a matrix has 5 elements, write all possible orders it can have.

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  15. If A=[[2, 3],[ 5,-2]], write A^(-1) in terms of A

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  16. Using properties of determinants, prove the following: |[1,x,x^2],[...

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  17. Write the projection of the vector hat i- hat j on the vector ha...

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  18. Write the direction-cosines of the line joining the points (1, 0, 0...

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  19. Differentiate the following function with respect to x : (log\ x)^...

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  20. If y=log[x+sqrt(x^2+a^2)\ ] , show that (x^2+a^2)(d^2\ y)/(dx^2)+x(dy)...

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