Let r be a real number and f(x) = {2x-r if x≥r; r if x<r}. Then, the equation f(x)=f(f(x)) holds for all real values of x where:
Question:
Let r be a real number and f(x) = {2x-r if x≥r; r if x<r}. Then, the equation f(x)=f(f(x)) holds for all real values of x where:
Let r be a real number and f(x) = {2x-r if x≥r; r if x<r}. Then, the equation f(x)=f(f(x)) holds for all real values of x where:
Options
Answer: x≤r
Explanation:
For x≥r: f(x)=2x-r. f(f(x))=f(2x-r). If 2x-r≥r, then f(2x-r)=2(2x-r)-r=4x-3r. For f(x)=f(f(x)): 2x-r=4x-3r, giving x=r. For x≥r, the condition holds.
Explanation:
For x≥r: f(x)=2x-r. f(f(x))=f(2x-r). If 2x-r≥r, then f(2x-r)=2(2x-r)-r=4x-3r. For f(x)=f(f(x)): 2x-r=4x-3r, giving x=r. For x≥r, the condition holds.
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