Question

Which of the following statements is/are true? Domain of $f\left(x\right)=log_{a} x \left(x, a \ge\,0\right)$ and $a\ne1$ is $\left(0, \infty\right)$ and range of $f\left(x\right)=R.$ Range of $f\left(x\right)=\sqrt{x} \forall\,x \,\ge0$ is $[0, \infty).$

• A. Only Statement-I
• B. Only Statement-II
• C. Both Statement-I and Statement-II
• D. Neither Statement-I nor Statement-II

Answer 1

Answer: (C)

Both Statement-I and Statement-II

Answer 2

$f\left(x\right)=log_{a} x; x, a>0; a\ne1$ or $f\left(x\right)=\frac{log\,x}{log \,a}$ Domain of $f\left(x\right)$ is $\left(0, \infty\right)$ Range of $f\left(x\right)$ is $\left(-\infty, \infty\right)$ or $R$ $f\left(x\right) =\sqrt{x}, x \ge0$ Range of $f\left(x\right)$ is $[0, \infty)$