Let A = 1 , 2 , 3 , … , 10 and f : A → A be defined as f k = k + 1 if k is odd k if k is even Then the number of possible functions g : A → A such that g o f = f is:

Question

Let A = 1 , 2 , 3 , &#8230; , 10 and f : A &#8594; A be defined as f k = k + 1 if k is odd k if k is even Then the number of possible functions g : A &#8594; A such that g o f = f is:

Quantrex Academy · Accepted Answer

Correct answer: D. 10 5

f x = x + 1 if &#160; x &#160; is odd x if &#160; x &#160; is even &#8757; &#160; g : A &#8594; A such that g f x = f x &#8658; If x is even then g x = x &#160; &#160; &#160; &#8230; 1 If x is odd then g x + 1 = x + 1 &#160; &#160; &#160; &#8230; 2 from 1 and 2 we can say that g x = x if x is even &#8658; If x is odd then g x can take any value in set A so number of g x = 10 5 &#215; 1

Let A = 1 , 2 , 3 , … , 10 and f : A → A be defined as f k = k + 1 if k is odd k if k is even Then the number of possible functions g : A → A such that g o f = f is:

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More from Functions

Let A = 1 , 2 , 3 , &#8230; , 10 and f : A &#8594; A be defined as f k = k + 1 if k is odd k if k is even Then the number of possible functions g : A &#8594; A such that g o f = f is:

Options

Correct answer

Step-by-step solution

More from Functions

Let A = 1 , 2 , 3 , … , 10 and f : A → A be defined as f k = k + 1 if k is odd k if k is even Then the number of possible functions g : A → A such that g o f = f is: