Question

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

1. $f\left(x\right)=-3x+4$
2. $f\left(x\right)=-3x^2+7$
3. role="math" localid="1668414131444" $f\left(x\right)=(x+1)/(\mathrm{x}+2)$
4. role="math" localid="1668414147841" $f\left(x\right)=x^5+1$

Short answer

1. Yes
2. No
3. No
4. Yes

\(\begin{array}{c}{{\rm{d}}_{\rm{1}}}{\rm{ = 123}}...{\rm{(n - 1)n}}\\{\rm{i = 1}}\end{array}\)

For \({\rm{m = 1}}\) to \({\rm{n}}\)

\({{\rm{a}}_{\rm{m}}}{\rm{ = m}}\)

While\({{\rm{d}}_{\rm{i}}} \ne n(n - 1)...321\)

\({\rm{i = i + 1, j = n - 1}}\)

Step-by-step solution

Step: 1

1. Yes
2. No
3. No
4. Yes