Question
The range of the function f(x)= 3 x^2-4 x+5 is
BITSAT
Mathematics
Quadratic Equation
2023
BITSAT 2023 (Memory Based Paper 1)
BITSAT Mathematics Question (2023) — Solution
Options
- A. (- , 11 3 ]
- B. (- , 11 5 )
- C. [ 11 3 , )
- D. ( 11 5 , ).
Answer
C. [ 11 3 , )
Step-by-step solution
f(x) is defined if 3 x^2-4 x+5 0 3 [x^2- 4 3 x+ 5 3 ] 0 3 [ (x- 2 3 )^2+ 11 9 ] 0 Which is true for all real x Domain of f(x)= (- , ) Let y= 3 x^2-4 x+5 y^2=3 x^2-4 x+5 i.e. 3 x^2-4 x+ (5-y^2 )=0 For x to be real , 16-12 (5-y^2 ) 0 y 11 3 Range of y= [ 11 3 , )
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