Solve this:Question No 7The range of the function fx =5x-x2-6 is A -12,12B 0,12C 0,12D 12,-12 - Maths - Relations and Functions

Question

Solve this: Question   No   7 The  
range   of   the   function   f x   = 5 x
- x 2 - 6   is   A   - 1 2 , 1 2 B   0 , 1 2 C
  0 , 1 2 D   1 2 , - 1 2

Aarushi Mishra · Accepted Answer

fx=5x-x2-6Quantity inside square root should be non-negative5x-x2-6≥0x2-5x+6≤0x2-2x-3x+6≤0xx-2-3x-2≤0x-2x-3≤0Solutions of x-ax-b≤0, where a<b is given by x∈a,bx∈2,3fx=5x-x2-6fx=-6-x2-5x+522-522fx=-6+522-x2-5x+522fx=-6+254-x+522fx=14-x+522Since x+522≥0, therefore 14-x+522 will be maximum when x+522=0
 fx will be maximum when x+522=0, i
e
 x=-52max fx=14=12f2=5×2-22-6=0=f1And we know 5x-x2-6≥0so min fx=0Since fx is continous so it will take all values between itRange=0,12

Solve this: Question No . 7 The range of the function f x = 5 x - x 2 - 6 is . A - 1 2 , 1 2 B 0 , 1 2 C 0 , 1 2 D 1 2 , - 1 2

Solve this: $Question No . 7 The range of the function f (x) = \sqrt{5 x - x^{2} - 6} is . (A) [- \frac{1}{2}, \frac{1}{2}] (B) [0, \frac{1}{2}] (C) (0, \frac{1}{2}) (D) (\frac{1}{2}, - \frac{1}{2})$