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?

Correct answer: A. 0 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

NDA 2025

Exam: NDA
Year: 2025
Subject: Mathematics
Chapter: Functions

NDA 2025 · Mathematics · Functions

For the following two (02) items: Consider the function f(x) = 10^x...

For the following two (02) items:
Consider the function

f(x) = \dfrac{10^x - 10^{-x}}{10^x + 10^{-x}}

.

What is

f {}^{\circ} f {}^{\circ} f {}^{\circ} f {}^{\circ} f(0)

equal to?

Options

A $0$
B $1$
C $5$
D $10$

Correct answer

A. $0$

Step-by-step solution

Given the function

f(x) = \dfrac{10^x - 10^{-x}}{10^x + 10^{-x}}

Substituting

x = 0

into the function:

f(0) = \dfrac{10^0 - 10^{-0}}{10^0 + 10^{-0}}

f(0) = \dfrac{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 {}^{\circ} f {}^{\circ} f {}^{\circ} f {}^{\circ} f(0) = 0

Answer:

0

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