MATH SOLVE

3 months ago

Q:
# Which of the following explains why f(x) = log4x does not have a y-intercept? Check all that apply.1. There is no power of 4 that is equal to 0.2. There is no power of 4 that is equal to 1.3. Its inverse does not have any x-intercepts.4. Its inverse does not have any y-intercepts.NEED ANSWER ASAP!!!!!

Accepted Solution

A:

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.