Aditya Gupta
Last Activity: 4 Years ago
y= f(x)= 6|x – 1|+|3x – 2|+2x
take cases:
- x lies in (-inf, 2/3]: so, y= 6(1 – x)+2 – 3x + 2x= 8 – 7x. so 7x lies in (-inf, 14/3] or – 7x lies in [–14/3, inf) or 8 – 7x lies in [10/3, inf).
- x lies in (2/3, 1]: so, y= 6(1 – x)+3x – 2+ 2x= 4 – x. so – x lies in [ – 1, – 2/3) or 4 – x lies in [3, 10/3).
- x lies in (1, inf): so, y= 6(x – 1)+3x – 2+ 2x= 11x – 8. so 11x lies in (11, inf) or 11x – 8 lies in (3, inf).
hence, the combined range of fn is union of these 3 sets.
so the range is [3, inf)
or a= 3
KINDLY APPROVE :))
