Math, asked by arsh23102002, 11 months ago

answer the 16 question

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Answered by anmolvoltp784kl
0

Answer:

Step-by-step explanation:

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Answered by Abhishek474241
2

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f:R->R f(x)=x3+x

Let x,y belongs to R

f(x)=f(y)

x3+x=y3+y

(x3-y3)+x-y=0

(x-y)(x2+xy+y2+1)=0

x=y

f(x)=f(y)

=) x=y for all x,y belongs to R

So, f is one-one function

Let y be any arbitrary element of R

f(x)=y

=) x3+x=y

x3+x-y=0

For every value of y, the equation x3+x-y=0 has a real root a (alpha)

a3+a-y=0

a3+a=y

f(a)=y

For every y belongs to R there exists a (alpha) belongs R such that f(a)=y

So, f is a onto function

Hence, f:R->R is a bijective function

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