I have the function $f(x) = 4|3x-1|+|6x+3|$
I am supposed to state the partial functions without the absolute value notation for the different intervals.
I know that for:
$$x\ge 1/3, f(x) = 18x-1$$ $$x < -1/2, f(x) = -18x+1$$
I reached this conclusion from calculating assuming $x<0, x \le 0$ and then adjusting for the coefficients for $x$.
However I am not sure how to calculate the function for the interval $-1/2 \le x < 1/3$
Thanks in advance!