Let f:R−{2,6}→R be real valued function defined as f(x)=x2−8x+12x2+2x+1. Then range of f is:
Explanation
Solution:
y=x2−8x+12x2+2x+1 lekar cross-multiply karein.
x mein quadratic equation banayein: x2(y−1)−x(8y+2)+(12y−1)=0.
Kyuki x real hai, isliye D≥0:
(8y+2)2−4(y−1)(12y−1)≥0.
Expand aur simplify karein: 64y2+32y+4−4(12y2−13y+1)≥0.
16y2+84y≥0⇒4y(4y+21)≥0.
Interval: y∈(−∞,−421]∪[0,∞).
Sahi Option: (4)
Explanation
Solution:
y=x2−8x+12x2+2x+1 lekar cross-multiply karein.
x mein quadratic equation banayein: x2(y−1)−x(8y+2)+(12y−1)=0.
Kyuki x real hai, isliye D≥0:
(8y+2)2−4(y−1)(12y−1)≥0.
Expand aur simplify karein: 64y2+32y+4−4(12y2−13y+1)≥0.
16y2+84y≥0⇒4y(4y+21)≥0.
Interval: y∈(−∞,−421]∪[0,∞).
Sahi Option: (4)
