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Let f : N to R be a function defined as...

Let `f : N to R` be a function defined as `f(x)=4x^(2)+12x +15`. Show that `f:N to S`, where S is the range of f, is invertible. Also, find the inverse of f.

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The correct Answer is:
`f^(-1)(x) = (-3 + sqrt(x - 6))/(2)`
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ARIHANT PRAKASHAN-VERY SIMILAR TEST 9-Section C
  1. Evaluate int (1)/(sinx(2cos^(2) x -1)) dx.

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  2. Prove analytically : The perpendicular bisector of the sides of a tria...

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  3. Find the foot of the perpendicular drawn from the point 2hati - hatj +...

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  4. Solve the following LPP graphically. Maximise Z = 5x + 3y Su...

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  5. Let f : N to R be a function defined as f(x)=4x^(2)+12x +15. Show tha...

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  6. If A = [(1, -1, 1),(2, 1, -3), (1, 1, 1)], find A^(-1) and hence solve...

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  7. A dice is thrown thrice. Find the probability of getting an odd number...

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  8. Find the inverse of the following matrix using elementary transformati...

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  9. If e^(x) + e^(y) = e^(x + y), then prove that (dy)/(dx) = (e^(x)(e^...

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  10. Find a point on the curve f(x)=(x-3)^2, where the tangent is parallel ...

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  11. Find the area of the region included between the parabolas y^(2) = 4ax...

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  12. Solve (dy)/(dx) = ysin 2x: y(0) = 1.

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  13. Evaluate int (1)/(sinx(2cos^(2) x -1)) dx.

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  14. Prove analytically : The perpendicular bisector of the sides of a tria...

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  15. Find the foot of the perpendicular drawn from the point 2hati - hatj +...

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  16. Solve the following LPP graphically. Maximise Z = 5x + 3y Su...

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  17. Let f : N to R be a function defined as f(x)=4x^(2)+12x +15. Show tha...

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  18. If A = [(1, -1, 1),(2, 1, -3), (1, 1, 1)], find A^(-1) and hence solve...

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  19. A die is tossed thrice. Find the probability of getting an even number...

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  20. Find the inverse of the following matrix using elementary transformati...

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