Original
Are
{{MATH_158}}
and
{{MATH_159}}
the same function?
{{CMD_160}}
Let's use a series of steps to think about this question.
First, what if we compare graphs? Here we see a graph of
{{MATH_161}}:
{{CMD_162}}
{{ENV_163}}
{{COMMENT_164}}
{{COMMENT_165}}
{{COMMENT_166}}
{{COMMENT_167}}
{{CMD_168}}
On the other hand, here is a graph of {{MATH_169}}:
{{CMD_170}}
{{ENV_171}}
{{COMMENT_172}}
{{COMMENT_173}}
{{COMMENT_174}}
{{COMMENT_175}}
{{CMD_176}}
Second, what if we compare the domains? We cannot evaluate {{MATH_177}} at
{{MATH_178}}. This is where {{MATH_179}} is undefined. On the other
hand, there is no value of {{MATH_180}} where we cannot evaluate {{MATH_181}}. In other
words, the domain of {{MATH_182}} is {{MATH_183}}.