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Functions · 2022 · 25 Jun · Shift 1

3 Mathematics questions from this JEE Main paper

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2022 · 25 Jun · Shift 1
Mathematics
Functions

Functions · 2022 · 25 Jun · Shift 1

3 Mathematics questions from this JEE Main paper

Q25.Let f : N $\to$ R be a function such that $f (x + y) = 2 f (x) f (y)$ for natural numbers x and y. If f(1) = 2, then the value of $α$ for which $k = 1 \sum 10 f (α + k) = \frac{512}{3} (2^{20} - 1)$ holds, is :
Mathematics · Functions · MCQ
Q33.Let $f : R \to R$ and $g : R \to R$ be two functions defined by $f (x) = lo g_{e} (x^{2} + 1) - e^{- x} + 1$ and $g (x) = \frac{1 - 2 e ^{2 x}}{e ^{x}}$ . Then, for which of the following range of $α$ , the inequality $f (g (\frac{( α - 1 ) ^{2}}{3})) > f (g (α - \frac{5}{3}))$ …
Mathematics · Functions · MCQ
Q42.Let $f : R \to R$ be a function defined by $f (x) = (2 (1 - \frac{x ^{25}}{2}) (2 + x^{25}))^{\frac{1}{50}}$ . If the function $g (x) = f (f (f (x))) + f (f (x))$ , then the greatest integer less than or equal…
Mathematics · Functions · Numerical