CameraIcon

SearchIcon

MyQuestionIcon

5

You visited us 5 times! Enjoying our articles? Unlock Full Access!

Definition of Sets

Let S = a,b,c...

Question

Let $S = {a, b, c}$ and $T = {1, 2, 3}$ . Find $F^{- 1}$ of the following function F from S to T, if it exists.

$(i) F = {(a, 3), (b, 2), (c, 1)}$

Open in App

Solution

We know that A function has inverse if it is one-one and onto.
F={(a, 3),(b, 2),(c, 1)}
Since each element has unique image,
F is one-one.
Since for every image, there is a corresponding element, F is onto.
Since, function is both one-one and onto it will have inverse.
F = {(a, 3),(b, 2), (c, 1)}
$F^{- 1} = (3, a), (2, b), (1, c)$

Suggest Corrections

thumbs-up

0

Similar questions

S = {a, b, c}

T = {1, 2, 3}

F^{- 1}

of the following functions

F

S

T

, if it exists
(i)

F = {(a, 3), (b, 2), (c, 1)}

F = {(a, 2), (b, 1), (c, 1)}

Let S = {a, b, c} and T = {1, 2, 3}. Find F⁻¹ of the following functions F from S to T, if it exists.

(i) F = {(a, 3), (b, 2), (c, 1)} (ii) F = {(a, 2), (b, 1), (c, 1)}

f

be a real valued function defined as

f (x) = x^{2} + x^{2} 1 \int - 1 t \cdot f (t) d t + x^{3} 1 \int - 1 f (t) d t .

Then which of the following hold(s) good ?

f (x) = \sqrt{x^{2} - 3 x + 2}

g (x) = \sqrt{x}

be two given functions . If

S

be the domain of

f \circ g

T

be the domain of

g \circ f

f

h

are relations from

A \to B

A = {a, b, c, d}

B = {s, t, u}

defined as follows:

f (a) = t, f (b) = s, f (c) = s, f (d) = u

h (a) = s, h (b) = t, h (c) = s, h (a) = u, h (d) = u

Which one of the following statement is true?

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Definition of Sets

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon