Let f: (0, ∞) → R be a twice differentiable function. If for some a ≠ 0, ∫₀¹ f(λ x) dλ = a f(x), f(1) = 1 and f(16) = 1/8, then 16 - f'(1/16) is equal to

Unclassified (maths): JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q122

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumUnclassified (maths)

Let

f: (0, \infty) \to \mathbf{R}

be a twice differentiable function. If for some

a \neq 0

\int_0^1 f(\lambda x) d\lambda = a f(x)

f(1) = 1

and

f(16) = \frac{1}{8}

, then

16 - f'\left(\frac{1}{16}\right)

is equal to

Your answerInteger or decimal