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Home==>exercise 1.3 (ncert class 12th maths)

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Asked: September 21, 2020In: NCERT 12th Maths

14. Let f : R – \{\frac{-4}{3}\} \to R be a function defined as f(x) = \frac{4x}{3x+4} The inverse of f is the map g : Range f \to R - \{\frac{-4}{3}\} given by

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(A) g(y) = (B) g(y) = (C) g(y) =

exercise 1.3 (ncert class 12th maths)ncertrelations and functions
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Asked: September 21, 2020In: NCERT 12th Maths

13. If f : R \to R be given by f (x) = (3 - x^3)^\frac{1}{3} , then f \circ f (x) is

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(A) (B) (C) x (D)

exercise 1.3 (ncert class 12th maths)ncertrelations and functions
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Asked: September 21, 2020In: NCERT 12th Maths

12. Let f : X \to Y be an invertible function. Show that the inverse of f^{ -1} is f, i.e., (f^{-1})^{-1} = f

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exercise 1.3 (ncert class 12th maths)ncertrelations and functions
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Asked: September 21, 2020In: NCERT 12th Maths

11. Consider f : \{1, 2, 3 \} \to \{a, b, c \} given by f(1) = a, f(2) = b and f(3) = c. Find f^{-1} and show that (f^{ -1})^{-1} = f.

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exercise 1.3 (ncert class 12th maths)ncertrelations and functions
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Asked: September 21, 2020In: NCERT 12th Maths

10. Let f : X \to Y be an invertible function. Show that f has unique inverse.

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(Hint: suppose and are two inverses of f. Then for all

exercise 1.3 (ncert class 12th maths)ncertrelations and functions
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Asked: September 21, 2020In: NCERT 12th Maths

9. Consider f : R_+\to [-5, \infty) given by f(x) = 9x^2 +6x-5 .Show that f is invertible with f ^{-1} (y) = ( \frac{(\sqrt{y+6})-1}{3} ) .

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exercise 1.3 (ncert class 12th maths)ncertrelations and functions
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Asked: September 21, 2020In: NCERT 12th Maths

8. Consider f : R_+ \to [4, ) 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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exercise 1.3 (ncert class 12th maths)ncertrelations and functions
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Asked: September 21, 2020In: NCERT 12th Maths

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

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exercise 1.3 (ncert class 12th maths)ncertrelations and functions
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Asked: September 21, 2020In: NCERT 12th Maths

6. Show that f : [-1, 1] \to R , given by f (x) = \frac{x}{x+2} is one-one. Find the inverse of the function f : [-1, 1] \to \text{Range} f.

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( Hint : For y Range f, y = f(x) = , for ...

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Asked: September 21, 2020In: NCERT 12th Maths

5. State with reason whether following functions have inverse

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(i)  f : {1, 2, 3, 4} {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)} (ii)  g : {5, 6, 7, 8}

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