[tex]c)f(x)=4\text{ log\lparen x+3\rparen}[/tex]
Explanation
to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.
[tex]\begin{gathered} f(x)\Rightarrow shifted\text{ b unit to left }\Rightarrow f(x+b) \\ f(x)\operatorname{\Rightarrow}sh\imaginaryI fted\text{ b units to right}\Rightarrow f(x-b) \end{gathered}[/tex]
Step 1
given
[tex]f(x)=4\text{ log \lparen x\rparen}[/tex]
if the function is shifted three units to the left then
[tex]\begin{gathered} b=3(positive) \\ \end{gathered}[/tex]
hence
[tex]\begin{gathered} g(x)=4\text{ log \lparen x\rparen}\Rightarrow shifted\text{ 3 units to left}\Rightarrow g(x+3)\Rightarrow f(x) \\ add\text{ x to the argument of the function} \\ f(x)=4\text{ log\lparen x+3\rparen} \end{gathered}[/tex]
therefore, the answer is
[tex]c)f(x)=4\text{ log\lparen x+3\rparen}[/tex]
I hope this helps you
