Mathematics

Problem

Define

h:\mathbb R\to\mathbb R

h(x)=\begin{cases}x+1,&x<0\\ x^{2}+k,&x\ge 0\end{cases}.

For which real values of

k

h

one-to-one on

\mathbb R

? a)

k<1

k=1

k\ge 1

d) All real

k