Question

How will you prove that f(a1)=f(a2) implies a1=a2 is a one to one function if a1 and a2 belongs to A

Answer 1

Answer:

$f(x^{3} )$    is a  1-1 function

Step-by-step explanation:

A function f(x) is said to be an injective or a 1-1 function, if

f(a) = f(b)  implies that a = b  for each a and b.

For example, $f(x^{3} )$  

here, the given function is 1-1  as,

f(1) = $1^{3}$  = 1

and f(-1) = $(-1)^{3}$  = -1

So, for a ≠ b, f(a)  ≠ f(b)

Hence, by definition, f($x^{3}$)  is a 1-1 function.