Question

Let A = {1, 3, 5, 7}, B = {1, 2, 3, 4, 5} define f(x) = x - 2 . Is f a function from A to B?

Answer 1

GIVEN :

Let the input values be A = {1, 3, 5, 7},and the output values be B = {1, 2, 3, 4, 5} define f(x) = x - 2 .

TO FIND :

Is f a function from A to B

SOLUTION :

Given that Let the input values be A = {1, 3, 5, 7},and the output values be  B = {1, 2, 3, 4, 5}

Also given that f define f(x) = x - 2 .

Now verify that the f is a function or not:

By the definition of a function: f is a relation from a set of input values to a set of possible output values where each input value is related to exactly one output value.

We can write the statement that f is a function from A to B by using the function notation f:A→B.

Since f(x)=x-2

we can put x=1,3,5,7 input values

f(1)=1-2=-1

f(3)=3-2=1

f(5)=5-2=3

f(7)=7-2=5

Hence we get output values are ${\{-1,1,3,5}\}$

While comparing the given output values with the above output values we get that , ${\{1,2,3,4,5}\}\neq {\{-1,1,3,5}\}$

∴ f does not assigns correct output values

∴ f is not well defined.

∴ f is not a function.