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The function f: R R is defined by f(x)=3^ -x . Observe the following statements of it I. f is one-one II. f is onto III. f is a decreasing function Out of these, true statement are

Options

  1. AOnly I, II
  2. BOnly II,III
  3. COnly I,III
  4. DI,II,III

Correct answer

A. Only I, II

Step-by-step solution

Since, f: R R such that f(x)=3^ -x . Let y₁ and y₂ be two elements of f(x) such that aligned & y₁=y₂ & 3^ -x₁ =3^ -x₂ x₁=x₂ & aligned Since, if two images are equal, then their elements are equal, therefore it is one-one function Let y=3^ -x On differentiating w.r.t. x , we get d y d x =-3^ -x 3 < 0 for every value of x It is decreasing function Statement I and II are true.

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