Question

If \(f(x)=\frac{2}{x+5}\) and \(g(x)=x^{2}-1\), then the positive value of \(x\) satisfying \((f\circ g)(x)=\frac{1}{10}\) is

• A. \(4\)
• B. \(2\)
• C. \(6\)
• D. \(16\)

Hint:

Compose f with g and solve the resulting equation.

Answer 1

The Correct Option is A

Step 1: Substitution Check
Put $x=4$: $g(4)=15$, and $f(15)=\dfrac{2}{20}=\dfrac{1}{10}$.

Step 2: Conclusion
So $x=4$, option (A).

Step 3: Result
Take the positive root, $x=4$.

Final Answer:
Option (A), 4. \[ \boxed{\text{(A) }4} \]