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AP EAMCET202420 May 2024Morning ShiftMathematicsFunctionsActual

Let a 1 and 0 b 1 . If f: R [0,1] is defined by f(x)= array l a^x,- x 0 b^x, 0 x array . then f(x) is

Options

  1. AA bijection
  2. BOne-one but not onto
  3. COnto but not one-one-
  4. DNeither one-one nor onto

Correct answer

D. Neither one-one nor onto

Step-by-step solution

f(x)= cases a^x, & - x 0 b^x, & 0 x cases a 1 and 0 b 1 So by the graph Clearly, every horizontal line cuts f(x) at 2 points. Also, for f(x)=0 There is no x R So, f(x) is neither one-one nor onto

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