Please solve this ques please attach the solution, please
Dear student,
The question provided by you has some error, So I have assumed the question as below,
The function f : [0, 3] → [1, 29], defined by f(x) = 2x³ - 15x² + 36x + 1, is ____
Solution:
f(x) = 2x³ - 15x² + 36x + 1
So, f'(x) = 6x² - 30x + 36
= 6(x² - 5x + 6)
= 6(x - 2)(x - 3)
f(x) is increasing in [0, 2] and decreasing in [2, 3].
f (x) is many one.
f(0) = 1
f(2) = 29
f(3) = 28
Range is [1, 29].
Hence, f (x) is many-one-onto.
So Option B is correct.
Regards.
The question provided by you has some error, So I have assumed the question as below,
The function f : [0, 3] → [1, 29], defined by f(x) = 2x³ - 15x² + 36x + 1, is ____
Solution:
f(x) = 2x³ - 15x² + 36x + 1
So, f'(x) = 6x² - 30x + 36
= 6(x² - 5x + 6)
= 6(x - 2)(x - 3)
f(x) is increasing in [0, 2] and decreasing in [2, 3].
f (x) is many one.
f(0) = 1
f(2) = 29
f(3) = 28
Range is [1, 29].
Hence, f (x) is many-one-onto.
So Option B is correct.
Regards.