exercise 1.3 (ncert class 12th maths) – eduhilfe

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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) =

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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)

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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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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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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

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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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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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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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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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