Consider the following function double f(double x) if ( abs(x*x - 3) Give a value q (to 2 decimals) such that f (q) will return q: …

Official answer: 1.73 (±0.01). Explanation: The base condition checks whether |x2 - 3| < 0.01. If it is satisfied, the function returns x directly without making any further recursive calls. For f(q) to immediately return q, the condition must hold for q: |q2 - 3| < 0.01 Notice that the recurrence update formula xn+1 = xn2 + 1.5xn = 12 (xn + 3xn ) is the standard Newton-Raphson method for finding 3. The exact fixed point is: q = 3 1.732 Checking q = 1.73: |1.732 - 3| = |2.9929 - 3| = 0.0071 < 0.01 Thus, any value in the range 1.72 to 1.74 is valid.

Programming and Data Structures · Recursion

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

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GATE CSE 2014 Set 2 Q40 · NAT · 2 marks

Consider the following function `double f(double x) { if ( abs(x*x - 3) < 0.01) return x; else return f(x/2 + 1.5/x); }` Give a value $q$ (to 2 decimals) such that $f (q)$ will return $q$ : _____.

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Key concept

Recursion

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How GATE tests Recursion

GATE tests Recursion primarily through direct execution tracing of recursive C code snippets, stack-unwinding behavior (pre-order vs. post-order execution), and termination/infinite recursion analysis. Questions frequently incorporate static variables, pointer/reference aliasing, mutual recursion, and tree/array traversals to test whether candidates can systematically maintain call frames. In recent years, the focus has expanded from standard tracing to higher-order mathematical characterizations (e.g., finding the smallest input or maximum output value of composed recurrences).

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Programming and Data Structures · Recursion

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

Take topic test

GATE CSE 2014 Set 2 Q40 · NAT · 2 marks

Consider the following function `double f(double x) { if ( abs(x*x - 3) < 0.01) return x; else return f(x/2 + 1.5/x); }` Give a value $q$ (to 2 decimals) such that $f (q)$ will return $q$ : _____.

Numerical answer

Enter a value to check

Key concept

Recursion

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Recursion

Full Recursion guide →

More on Recursion

All 19 questions on Recursion →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Consider the following function `double f(double x) { if ( abs(x*x - 3) < 0.01) return x; else return f(x/2 + 1.5/x); }` Give a value $q$ (to 2 decimals) such that $f (q)$ will return $q$ : _____.

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Consider the following function `double f(double x) { if ( abs(x*x - 3) < 0.01) return x; else return f(x/2 + 1.5/x); }` Give a value $q$ (to 2 decimals) such that $f (q)$ will return $q$ : _____.

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Consider the following function double f(double x) { if ( abs(x*x - 3) < 0.01) return x; else return f(x/2 + 1.5/x); } Give a value qqq (to 2 decimals) such that f(q)f (q)f(q) will return qqq: _____.

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Consider the following function double f(double x) { if ( abs(x*x - 3) < 0.01) return x; else return f(x/2 + 1.5/x); } Give a value qqq (to 2 decimals) such that f(q)f (q)f(q) will return qqq: _____.

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Check you can still solve Recursion under a clock

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Consider the following function `double f(double x) { if ( abs(x*x - 3) < 0.01) return x; else return f(x/2 + 1.5/x); }` Give a value $q$ (to 2 decimals) such that $f (q)$ will return $q$ : _____.

Consider the following function `double f(double x) { if ( abs(x*x - 3) < 0.01) return x; else return f(x/2 + 1.5/x); }` Give a value $q$ (to 2 decimals) such that $f (q)$ will return $q$ : _____.