if f is strictly increasing, then which is necessarily WRONG
A.xf(2x)=2f(x)
B.integral f(x)dx from 0 to 1=integral fx(dx) from 1 to 2
dumplinghao123 wrote:if f is strictly increasing, then which is necessarily WRONG
A.xf(2x)=2f(x)
B.integral f(x)dx from 0 to 1=integral fx(dx) from 1 to 2
tarheel wrote:dumplinghao123 wrote:if f is strictly increasing, then which is necessarily WRONG
A.xf(2x)=2f(x)
B.integral f(x)dx from 0 to 1=integral fx(dx) from 1 to 2
The first one is necessarily wrong.
Let x=2, then A gives 2f(4)=2f(2), which is f(4)=f(2). But since f is strictly increasing, f(4)>f(2). Therefore A is wrong for all f.
dumplinghao123 wrote:Thanks!
But is there an couterexample for 2?
tarheel wrote:dumplinghao123 wrote:Thanks!
But is there an couterexample for 2?
Just make sure B says
Right?
If my interpretation is correct, it should be false. Since is strictly increasing,
dumplinghao123 wrote:Yea. The question ask what is necessarily wrong. So why not choose 2?
tarheel wrote:
The first one is necessarily wrong.
Let x=2, then A gives 2f(4)=2f(2), which is f(4)=f(2). But since f is strictly increasing, f(4)>f(2). Therefore A is wrong for all f.
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