Question

f: R—>R,f(x)= 2-3x, Is the given function one-one or onto?

Answer 1

f : R -------> R , f(x) = 2 - 3x

condition of one - one function :
if we take two different points x1 and x2 from domain of given function , f(x).
if we solve f(x1) = f(x2) , we get x1 = x2 then, f(x) is definitely an one one function.

let's take two different points x1 and x2
now, f(x1) = 2 - 3x1
f(x2) = 2 - 3x2

so, f(x1) = f(x2)
2 - 3x1 = 2 - 3x1
-3x1 = 3x2
x1 = x2
hence, it is clear that function is one - one.

condition of onto function :
co - domain = range

let's find range ,
y = 2 - 3x
3x = 2 - y
x = f(y) = (2 - y)/3
hence, domain of f(y) belongs to R
so, range of f(x) belongs to R
hence, co-domain = range
so, f(x) is onto function.

hence, function,f(x) is one - one as well as onto.