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Consider f: R^+->[4,\ oo) given by f(x)=...

Consider `f: R^+->[4,\ oo)` given by `f(x)=x^2+4` . Show that `f` is invertible with inverse `f^(-1)dot`

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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.

Consider f\ : R_+vec[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.

Consider f: R->R given by f(x) = 4x + 3 . Show that f is invertible. Find the inverse of f .

Consider f: R->R given by f(x) = 4x + 3 . Show that f is invertible. Find the inverse of f.

Consider f: R_+->[-5,oo) given by f(x)=9x^2+6x-5 . Show that f is invertible with f^(-1)(y)=(((sqrt(y+6))-1)/3)

Consider f: R rarr [-5,oo) given by f(x)=9x^2+6x-5 . Show that f is invertible with f^(-1)(y)=((sqrt(y+6)-1)/3)dot

Consider f:R_+->[-9,oo[ given by f(x)=5x^2+6x-9 . Prove that f is invertible with f^(-1)(y)=(sqrt(54+5y)-3)/5

Let f: R->R be defined by f(x)=3x-7 . Show that f is invertible and hence find f^(-1) .

Consider f : R->{-4/3}->R-{4/3} given by f(x) = (4x+3)/(3x+4) . Show that f is bijective. Find the inverse of f and hence find f^(-1)(0) and x such that f^-1(x) = 2 .

Let f:[-1,oo]vec[-1,) is given by f(x)=(x+1)^2-1,xgeq-1. Show that f is invertible. Also, find the set S={x :f(x)=f^(-1)(x)}dot

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Find the value of tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))

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  2. Using properties of determinants, prove the following |[x,x+y,x+2y],[x...

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  3. Consider f: R^+->[4,\ oo) given by f(x)=x^2+4 . Show that f is inverti...

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  4. Differentiate the following with respect to x : sin^(-1)((2^(x+1). 3^x...

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  5. If y^x=e^(y-x), prove that (dy)/(dx)=((1+logy)^2)/(logy)

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  6. Write the cartesian equation of a plane, bisecting the line segment...

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  7. Solve the following differential equation: y\ dx+xlog(y/x)dy=2x\ dy

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  8. Find the particular solution of the following differential equation...

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  9. Write the value of sin[pi/3-sin^(-1)(-1/2)]

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  10. For a\ 2\ xx\ 2\ matrix, A=[a(i j)], whose elements are given by a...

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  11. Evaluate: int1^3(2x^2+5x)dx as limit of a sum

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  12. State the reason for the relation R in the set {1, 2, 3} given by R=...

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  13. Write the value of intsecx\ (secx+tanx)\ dx

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  14. Write the value of int(dx)/(x^2+16)

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  15. For what value of x, the matrix [(5-x,x+1),(2,4)] is singular?

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  16. Write A^-1 for A=[(2,5),(1,3)]

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  17. For what value of a the vectors 2 hat i-\ 3 hat j+4 hat k and a h...

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  18. Write the direction cosines of the vector -2 hat i+ hat j-5 hat k

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  19. The length x of a rectangle is decreasing at the rate of 5 cm/minute...

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  20. Find the intervals in which the function f given f(x)=\ sin x+cosx ,\...

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