How do you find the domain of $f(x)= ln(4x +3)$ ?

Question

10006 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-22T13:19:36

$x> -3/4$

As $f(x)=ln(4x+3)$ and we cannot have natural log of a negative number as also $0$ , the domain is given by $4x+3>0$ or $x> -3/4$ .

This may also be seen by the graph of $f(x)=ln(4x+3)$

graph{ln(4x+3) [-10, 10, -5, 5]}

Answer 2 · 2017-10-22T13:20:18

Write an inequality that asserts that the argument of the logarithm must be greater than zero and then solve for x.

Write the inequality

$4x+3>0$

Subtract 3 from both sides:

$4x > -3$

Divide both sides by 4:

$x > -3/4$

The domain is ${x in RR: x > -3/4}$ .

How do you find the domain of f(x)= ln(4x +3)f(x)= ln(4x +3)?