Question

gof तथा fog ज्ञात कीजिए, यदि
(i) f (x) = | x | तथा g (x) =|5 x – 2|
(ii) f (x) = 8x³ तथा g (x) = x¹៸³

Answer 1

Given : (i) f (x) = | x | तथा g (x) =|5 x – 2|

To find :   gof तथा fog ज्ञात कीजिए,

Solution :

f (x) = | x |

g (x) =|5 x – 2|

gof (x) = g(f (x))

g(x) = |5 x – 2|

=> g(fx))  = | 5f(x) - 2|

f (x) = | x |

=> g(fx))  =  | 5|x| - 2|

=> gof   = | 5 |x|  - 2 |

fog(x) = f(g (x))

f (x) = | x |

=> f(g(x) = | g(x) |

g(x) = |5 x – 2|

=> f(g(x)  = |  |5 x – 2| |

=> f(g(x)   =  | 5 x  - 2 |

=> fog =  | 5 x  - 2 |

और सीखें :

gof ज्ञात कीजिए।

https://brainly.in/question/16554907

निम्नलिखित फलनों की एकैक (Injective) तथा आच्छादी (Surjective) गुणों की जाँच

https://brainly.in/question/16549721

फलन R⟶R, न तो एकैकी है और न आच्छादक है,

https://brainly.in/question/16550005

सिद्ध कीजिए कि   (f + g) oh = foh + goh

https://brainly.in/question/16554901

Answer 2

Step-by-step explanation:

Solution:

The relation R defined on the set A;

(i) reflexive - is called if (a, a) ∈ R for every a ∈ A

(ii) is called symmetric if all a₁, a₂ ∈ for A (a₁, a₂) ∈ it happens

(iii) is called transitive if all a₁, a₂. For (a₁, a₃) ∈ R and (a₂, a₃) ∈ R for (a₁, a₃) ∈ R for a ₃∈ A

If the relation R is spontaneous, symmetric and contagious

R = {1, 2, 3}

R = {(1, 2), (2, 1)},

Reflexive:

If (a, a) ∈ R

But (1, 1) ∉ R

=> Relationship is not automatic

Symmetric

(a₁, a₂) ∈ R to (a₂, a₁) ∈ R

(1, 2) ∈ R (2, 1) ∈ R

=> For all a₁, a₂ ∈ A (a₁, a₂) from ∈ R (a₂, a₁) ∈ R

=> Relation is symmetric

Transitive

a₁, a₂. For (a₁, a₃) ∈ R and (a₂, a₃) ∈ R for (a₁, a₃) ∈ R for a ₃∈ A

(1, 2) ∈ R

(2, 1) ∈ R

But (1, 1) ∉ R

 All a₁, a₂. (a₁, a₃) for ₃∈ R and (a₂, a₃) for से R from (a₁, a₃) ∈ R not obtained

=> Relationship is not contagious

=> The relation R = {(1, 2), (2, 1)} is symmetric but neither spontaneous nor contagious.

QED

Iti siddham