Question

f(x)=|x+3|. Find all solutions to f(x-1)=x+4

Answer 1

\[f(x)=|x+3|,f(x-1)=?\]

Answer 2

the question on the homework is as stated. Where f(x-1)=x+4.
I'm not sure where to start

Answer 3

is it |x+3|-1=x+4 ?

Answer 4

bno

Answer 5

it is
\[f(x-1)+|x-1+3|=|x+2|\]

Answer 6

\[f(\color{red}{x}) = |\color{red}{x}+3|\]So \(f(\color{red}{x-1})= |\color{red}{x-1}+3|=\underline{\underline{\underline{|x+2|}}}\)

Answer 7

\underline\underline\underline
i like it

Answer 8

oh... so where does the x+4 come in?

Answer 9

oh.. |x+2|=x+4 solve x

Answer 10

Yeah, so you "split" it into two cases, one where x+2 is positive and another one where x+2 is negative, so you have two equation to solve:

\(x+2 = x+4\\x+2=-(x+4)\)

Does that make sense?

Answer 11

click. thank you. makes sense.