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If f : R → R defined by f(x) = \(\frac{3 x+5}{2}\) is an invertible function, then find f-1.

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Let f : R → R, g : R → R be two functions such that f(x) = 2x – 3, g(x) = x3 + 5. The function (fog)-1 (x) is

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If * is a binary operation on set of integers I defined by a * b = 3a + 4b – 2, then find the value of 4 * 5.

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Let * be the binary operation on N given by a * b = HCF (a, b) where, a, b ∈ N. Find the value of 22 * 4

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Consider the binary operation * on Q defind by a * b = a + 12b + ab for a, b ∈ Q. Find 2 * \(\frac{1}{3}\) (

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The domain of the function \(f(x)=\frac{1}{\sqrt{\{\sin x\}+\{\sin (\pi+x)\}}}\) where {.}

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Range of \(f(x)=\sqrt{(1-\cos x) \sqrt{(1-\cos x) \sqrt{(1-\cos x) \ldots \ldots \infty}}}\)

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Let * be a binary operation on set Q of rational numbers defined as

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The number of binary operations that can be defined on a set of 2 elements is (a) 8 (b) 4 (c) 16 (d) 64

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If the binary operation * is defind on the set Q+ of all positive rational numbers by a * b

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If f : R → R, g : R → R and h : R → R are such that f(x) = x2, g(x) = tan x and h(x) = log x,

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If f(x) = \(1-\frac{1}{x}\), then f(f(\(\frac{1}{x}\))) (a) \(\frac{1}{x}\) (b) \(\frac{1}{1+x}\)

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Let \(f(x)=\frac{x-1}{x+1}\), then f(f(x)) is (a) \(\frac{1}{x}\) (b) \(-\frac{1}{x}\)

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