Find the range of the function $f(x) = |x-4| + |x-20| + |x-50|,$ where $x$ is a real number.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the range of the function $f(x) = |x-4| + |x-20| + |x-50|,$ where $x$ is a real number.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
[46, \infty)
Find the range of the function $f(x) = |x-4| + |x-20| + |x-50|,$ where $x$ is a real number.
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