Question

prove that function f:R-R given by f(x)=2x, is one-one and onto​

Answer 1

f(x)=2x

one -one

f(x1)=2x1

f(x2)=2x2

putting

f(x1)=f(x2)

2x1=2x2

x1=x2

hence if f(x1)=f(x2), x1=x2

therefore function f is one -one

onto,

f(x)=2x

let f(x)=y, such that y€R

2x=y

x=y/2

since y is a real number,

h3nce y/2 will also be a real number so, x will also bea real number, i.e,. x€R

hence, f is onto