Determine whether each of these functions is a bijection from R to R. a) f (x)

Joni Kenny 2021-09-07 Answered

Whether each of these functions is a bijection from R to R.

a) f(x)=3x+4

b) f(x)=3x2+7

c) f(x)=x+1x+2
d)f(x)=x5+1

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Expert Answer

Ayesha Gomez
Answered 2021-09-08 Author has 104 answers

Part a-
f(x)=3x+4 is a bijection.
It is one-to-one as f(x)=f(y)3x+4=3y+4x=y
It is onto as f(4x3)=x
Part b-
f(x)=f(x).

The function is not a bijection as a result.
Part c-
No real number exists that is such that f(x)=x+1x+2=1. Hence the function is not a bijection.
Part d-
f(x)=x5+1 is a bijection.
It is a strictly increasing function.
Result:
Part a - Yes
Part b - NO
Part c - No
Part d - Yes

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