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

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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}#.