a Consider function y 2x What are its domain and range Is i

Solution

a)f(x)y=2x

there is no restrict on X so, domain is R(-,)

so ,similarly, range is R(-,)

let

f(x)=f(z)

2x=2z

=> x=z

therefore is one to one function.

y=2x

x=y/2

f(x)=y

x=f^-1(y)

f^-1(y)=y/2

inverse f^-1(x)=x/2

b)y=x²

there is no restrict on X so, domain is R(-,)

but for any X , y>0 as it is x² which is always positive.

therefore range [0,)

f(-1)=f(1)=1

but 1 -1

it is not one to one & no inverse.