Answer:
The value of f(4) is 5. We can write f(4) = 5.
Step-by-step explanation:
Since it is given that
[tex]\lim_{x\rightarrow 4}[3f(x)+f(x)g(x)]=45[/tex]
This is only possible if both the functions f(x) and g(x) are continuous at x = 4.
Now since the functions are continuous at x = 4 they need to be defined at the said value in accordance with the definition of continuous function.
Thus to obtain the limit we just put x = 4 in left hand side of the given relation thus getting
[tex][3f(4)+f(4)g(4)]=45..........(i)[/tex]
Now applying the given value of g(4) in equation 'i' we get
[tex]3f(4)+6f(4)=45\\\\9f(4)=45\\\\\therefore f(4)=\frac{45}{9}=5[/tex]
