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Simora [160]
3 years ago
10

F(x)=2x- 1 what is odd number

Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
5 0
Either the question is wrong or it is must be "for all positive integers number" .  Because for real number there are examples where it is not true . For example x = 1/2 it gives 0 which is a even number . For all positive integers the statement is true by following proof :

<span>f(x) = 2x-1 </span>
<span>f(x)%2 = (2x-1)%2 = (2x-1+2)%2 = (2x+1)%2 = ((2*(x%2))%2 + 1)%2 </span>

<span>now x%2 is either 1 or 0 </span>
<span>for x%2 = 1 </span>
f(x)%2 =  ((2*(1))%2 +1)%2 = (2%2+1)%2 = 1

for x%2 = 0
f(x)%2 = ((2*(0))%2 + 1)%2 = (0+1)%2 = 1

So in all cases f(x)%2 = 1 so f(x) must be odd for all positive integers

Here is another proof by mathematical induction :

<span>let x = 1 be base condition then </span>

<span>f(1) = 1 so it is true  for that </span>

<span>Lets assume f(x) is odd </span>

then f(x+1) = 2(x+1)-1

f(x+1) = 2x+2-1
f(x+1) = 2x+1
<span>f(x+1) = 2x-1 + 2 </span>
<span>f(x+1) = f(x) + 2  </span>
<span>f(x) = odd </span>
<span>so f(x) + 2  must be odd.</span>
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