You don't But your function can be inverted nevertheless: just write an equation ([imath]|x+1|+|2x+4| + 4x = a[/imath]) and solve it for x, which will give you [imath]x[/imath] as a function of [imath]a[/imath].How do I find the inverse of an absolute?
but won't i have multiple possibilities?You don't But your function can be inverted nevertheless: just write an equation ([imath]|x+1|+|2x+4| + 4x = a[/imath]) and solve it for x, which will give you [imath]x[/imath] as a function of [imath]a[/imath].
I believe you will not. If you draw the function's graph you will see that it is piecewise linear and monotone. Solving it separately for each of the linear pieces will get you the answer.but won't i have multiple possibilities?
I got three answers for x. What now?I believe you will not. If you draw the function's graph you will see that it is piecewise linear and monotone. Solving it separately for each of the linear pieces will get you the answer.
hm interesting, give me a minute to see if i get this.[imath]f(x) = |x+1| + 2|x+2| + 4x[/imath]
[imath]x \ge -1 \implies f(x) = 7x+5 \implies f(-1)=-2 \implies f^{-1}(-2) = -1 \text{ and } f(0)=5 \implies f^{-1}(5) = 0[/imath]
[imath]x \le -2 \implies f(x) = x-5 \implies f(-2) = -7 \implies f^{-1}(-7) = -2[/imath]
yeah i don't get it. how did you know in which one to put what values to get what you need for inverse functions???[imath]f(x) = |x+1| + 2|x+2| + 4x[/imath]
[imath]x \ge -1 \implies f(x) = 7x+5 \implies f(-1)=-2 \implies f^{-1}(-2) = -1 \text{ and } f(0)=5 \implies f^{-1}(5) = 0[/imath]
[imath]x \le -2 \implies f(x) = x-5 \implies f(-2) = -7 \implies f^{-1}(-7) = -2[/imath]
Write it out as a piece-wise function.yeah i don't get it. how did you know in which one to put what values to get what you need for inverse functions???
yes
okay thanks!