Question

Find all values for the variable x such that f(x) = x.f(x) = 4x - 1x=

Answer 1

`x=(1)/(3)`

1) In this problem, the point is to find all values in each y=x.

2) So, let's do the following:

`\begin{gathered} f(x)=4x-1 \\ \\ y=4x-1\:\:Plug\:y=x\:into\:that \\ \\ x=4x-1 \\ \\ x-4x=-1 \\ \\ -3x=-1 \\ \\ (-3x)/(-3)=(-1)/(-3) \\ \\ x=(1)/(3)\:\:Plug\:x=(1)/(3)\:into\:f(x)=4x-1\: \\ \\ y=4((1)/(3))-1 \\ \\ y=(4)/(3)-1\:\:\:Rewrite\:1\;as\:a\:fraction \\ \\ y=(4)/(3)-(3)/(3) \\ \\ y=(1)/(3) \\ \end{gathered}`

2) Thus, we can tell that the answer is:

`x=(1)/(3)`

Note: at x=1/3 y=1/3 what makes valid the condition f(x)=x