The range of the function f(x)=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 ) = (– ∞, ∞) Let y=3x2−4x+5⇒ y2 = 3x2 – 4x + 5 i.e. 3x2 – 4x + (5 – y2) = 0For x to be real, 16 – 12 (5 – y2) ≥ 0 ⇒y≥113∴ Range of y=113,∞