Find the domain of the function

Question

Given the function f(x)=log (5-8x)

a. find the domain of the function in set notation

b. solve the function when f(x)=0

Answer 1

f(x) = log(5-8x)

 

The argument.. (the part in the parenthesis here) ....

must be positive....  for lob_ba   a>0

This means that:  5-8x>0

 

5-8x>0

5>8x

x < 5/8

 

The domain of your function is all x<5/8

 

In interval notation  D = (-∞, 5/8)

 

Or D is {x: x ∈ R, x<5/8}

 

This is 3 ways of stating the answer which is simply

the domain is all x such that x is a real number less than 5/8

 

b.  log(5-8x)=0

     10⁰ = 5-8x

     1 = 5-8x

      8x = 4

      x = 1/2

 

This makes sense because log(1)=0 means 10⁰=1