Question
For the following two (02) items: Consider the function f(x) = 10^x - 10^ -x 10^x + 10^ -x . What is f f f f f(0) equal to?
NDA
Mathematics
Functions
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 0
- B. 1
- C. 5
- D. 10
Answer
A. 0
Step-by-step solution
Given the function f(x) = 10^x - 10^ -x 10^x + 10^ -x Substituting x = 0 into the function: f(0) = 10^0 - 10^ -0 10^0 + 10^ -0 f(0) = 1 - 1 1 + 1 = 0 Since f(0) = 0, applying the function f repeatedly to 0 will always result in 0. f(f(0)) = f(0) = 0 f(f(f(0))) = f(0) = 0 f(f(f(f(0)))) = f(0) = 0 f(f(f(f(f(0))))) = f(0) = 0 Therefore, f f f f f(0) = 0 Answer: 0
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