Question

For the given f(x), solve the equation f(x)=0 analytically and then use a graph of y=f(x) to solve the inequalities f(x)<0 and f(x)≥0. f(x)=ln(x+3)(1) What is the solution of f(x)=0?(2) What is the solution of f(x)<0?(3) What is the solution of f(x)≥0?

Answer 1

Step-by-step explanation:

f(x) is a logarithmic function. Logarithmic functions are zero when the argument is 1:

`\begin{gathered} f(x)=\ln (x+3)=0 \\ x+3=1 \\ x=1-3 \\ x=-2 \end{gathered}`

For greater values, the function is positive and for less values the function is negative.

Answers:

(1) x = -2

(2) x < -2. In interval notation x:(-∞, -2)

(3) x ≥ -2. In interval notation x:[-2, ∞)