Solution:
Given:
[tex]\begin{gathered} f(x)=log(x) \\ g(x)=log(x+4) \end{gathered}[/tex]From the equations of the functions, it can be seen that g(x) is a shift of 4 units to the left from f(x).
Hence,
The x-intercept occurs when y = 0
The x-intercept of f(x) is;
[tex]\begin{gathered} f(x)=log(x) \\ when\text{ f\lparen x\rparen = 0} \\ 0=log(x) \\ 10^0=x \\ x=1 \\ \\ Hence,\text{ the x-intercept of f\lparen x\rparen is 1} \\ x-intercept\text{ is at the point \lparen1,0\rparen} \end{gathered}[/tex]Since g(x) is a shift of 4 units left from f(x), then the x-intercept of g(x) will be;
[tex]\begin{gathered} x-intercept\text{ of }f(x)\text{ is }(1,0) \\ x-intercept\text{ of g\lparen x\rparen is }(1-4,0) \\ =(-3,0) \end{gathered}[/tex]Also, plotting the graphs of both functions, the x-intercept is shown.
Therefore, the x-intercept of g(x) is (-3,0)
