Question

Identify the function based on the given information.

1. Domain of the function is $R^{+}$

2. $F(x_1.x_2)=F\left(x_1\right)+F\left(x_2\right)$

3. $F\left(\frac{x_1}{x_2}\right)=F\left(x_1\right)-F\left(x_2\right)$

4. $F\left(1\right)=0$

5. $F\left(2^m\right)$ is proportional to m.

6. Range of function is R

• A. Logarithm Function
• B. Exponential Function
• C. Absolute value function
• D.

Answer 1

The correct option is A

Logarithm Function

Based on given information

Domain of Function is $R^{+}or(0,\infty )$

From the given options, we can guess it can be either logarithm function

or $\sqrt{x}$ because domain for other function is R NOT $(0,\infty )$

2.$F(x_1,x_2)=F\left(x_1\right)+F\left(x_2\right)$

It is the property of logarithm function

$lo{g}_{10}ab=lo{g}_{10}a+lo{g}_{10}b$

So,it should be a logarithm function

Other statements also validate the points.

3.$log\left(\frac{a}{b}\right)=loga-logb$

4.$Lo{g}_{10}\left(1\right)=0$

5.$log{2}^m=mlog2$

$log{2}^m$ is proportional to m

7. Range of logarithm Function is R or $(-\infty ,\infty )$

Graph of $lo{g}_{m}xwhenm>1$

Graph of $lo{g}_{m}x$ when $0<m<1$