The range of the function f (x) = loge (3x2 – 4x + 5) is

f (x) is defined if 3x2 – 4x + 5 > 0⇒3x2−43x+53>0⇒3x−232+119>0which is true for all real x.∴ Domain ( f ) = (– ∞, ∞)y=loge⁡3x2−4x+5⇒ey=3x2−4x+5 ⇒3x2−4x+5−ey=0For x to be real,16−125−ey≥0⇒12ey≥44⇒ey≥113 ⇒y≥loge⁡113∴ Range of f=loge⁡113,∞