Question

For the given functions, state the domain using an appropriate notation and evaluate f(2)

Answer 1

Given the equation:

`f(x)=\log _4x`

the given equation is for logarithm function with a base of 4

The domain will be all real numbers of x

So,

`Domain=(0,\infty)`

We will find the value of f(2)

So, substitute with x = 2 and solve

so,

`\begin{gathered} f(2)=\log _42 \\ 2=\sqrt[]{4}=4^{(1)/(2)} \\ \\ f(2)=\log _42=\log _44^{(1)/(2)}=(1)/(2)\cdot\log _44=(1)/(2)\cdot1=(1)/(2) \end{gathered}`

So, the answer will be:

`f(2)=(1)/(2)`