Problem-42

Problem-42

Determine whether each of these functions is a bijection from R to R.

a) f(x)= $x^{7}$ +1

b) f(x)=−5x+6

c) f(x)=− $6x^{2}$ +7

d) f(x)=x+ $\frac{1}{x}$ +4

Solution

a) f(x)= $x^{7}$ +1

f is a bijection from R to R.

b) f(x)=−5x+6

f is a bijection from R to R.

c) f(x)=− $6x^{2}$ +7

f is not a bijection from R to R.

d) f(x)=x+ $\frac{1}{x}$ +4

f is not a bijection from R to R