Answer:
The correct options are 1 and 3.
Step-by-step explanation:
The given function is
[tex]f(x)=log_4x[/tex]
It can be written as
[tex]y=log_4x[/tex]
[tex]4^y=x[/tex] .... (1) [tex][\because y=log_ax\Rightarrow a^y=x][/tex]
At y-intercept, the value of x is 0.
[tex]4^y=0[/tex]
For any value of y, this statement is not true. It means there is no power of 4 that is equal to 0.
Option 1 is correct.
Interchange x and y in equation 1 to find the inverse of the function.
[tex]4^x=y[/tex]
This function does not have any x-intercepts. because for any value of x, the value of y can not be 0.
Since the inverse function have not x-intercept, therefore the function have no y-intercept.
Option 3 is correct.
