Single correct option
If f(x) = (2x + 3)/(x − 2) for x ≠ 2, then f(f(f(5))) equals
- A. 5
- B. 13/3
- C. 3/13
- D. 7/3
Show answer and solution
Answer: (B) 13/3
Compute f(f(x)): substituting, numerator = 2(2x + 3)/(x − 2) + 3 = (7x)/(x − 2); denominator = (2x + 3)/(x − 2) − 2 = 7/(x − 2). So f(f(x)) = x — the function is its own inverse.
Hence f(f(f(5))) = f(5) = (10 + 3)/(5 − 2) = 13/3.
Tip: any f(x) = (ax + b)/(cx − a) satisfies f(f(x)) = x. Spotting this saves three substitutions.
Hence f(f(f(5))) = f(5) = (10 + 3)/(5 − 2) = 13/3.
Tip: any f(x) = (ax + b)/(cx − a) satisfies f(f(x)) = x. Spotting this saves three substitutions.
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