Q109 / 180 · KCET 2014 · Mathematics

Which one of the following is not correct for the features of exponential function given by
\( \mathrm{f}(x)=b^{x} \) where \( \mathrm{b}>1 ? \)

  • A
    The domain of the function is \( R \), the set of real numbers.
  • B
    The range of the function is the set of all positive real numbers.
  • C
    For very large negative values of \( x \), the function is very close to \( 0 \).
  • Correct answer
    D
    The point \( (1,0) \) is always on the graph of the function.

Solution

Given function $f(x)=b^{x}$ Let $y=b^{x} \rightarrow(1)$ At $x=0$, we have $y=1$ At $x=1$, we have $y=b$ So, $(1,0)$ does not satisfy equation (1) Hence,option (4) is not correct

Hence, the correct answer is option: 'D'.

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