The correct option is C A={x∈R:−2<x<∞};
R(f)={x∈R:−∞<x<log34}
3f(x)+2−x=4
⇒3f(x)=4−2−x
⇒f(x)=log3(4−2−x)
For domain
4−2−x>0
⇒2−x<22
⇒−x<2 [∵For a>1,ax<ay⇒x<y]
⇒x>−2
∴ Domain ={x∈R:−2<x<∞}
Now, −2<x<∞
⇒−∞<−x<2
⇒0<2−x<4
⇒0<4−2−x<4
Since, logax is strictly increasing for a>1, we get
−∞<log3(4−2−x)<log34
∴R(f)={x∈R:−∞<x<log34}