Find the inverse:
f(x)=2x-1/3

Question

Find the inverse: 
f(x)=2x-1/3

satellite73 · Answer

assuming it is $$\frac{2x-1}{3}$$, solve $$x=\frac{2y-1}{3}$$for $y$

satellite73 · Answer

any idea how to do that?

shaleiah · Answer

no :(

satellite73 · Answer

ok could you do it with numbers ? solve for $y$ $$\frac{2y-1}{3}=7$$ for example

shaleiah · Answer

y=11?

satellite73 · Answer

i don't know, i didn't do it
but the first step is to multiply both sides by 3, to get $$2y-1=3\times 7$$

satellite73 · Answer

then add one, get $$2y=22$$ 
then divide by 2, get $y=11$ so you are right

satellite73 · Answer

now lets repeat with variables, the procedure is the same

mathmale · Answer

Would you please draw this equation, f(x)=2x-1/3, so that all involved here can be absolutely sure we're on the same wavelength?

satellite73 · Answer

$$\frac{2y-1}{3}=x$$ first multiply both sides by $3$

mathmale · Answer

Note that satellite73 had to ask for clarification, and I too wondered what you meant.

shaleiah · Answer

this symbol "/" means division :) @mathmale

mathmale · Answer

As if I didn't know.

But did you mean f(x)=2x-1/3 as in
$$f(x)=2x-\frac{ 1 }{ 3 },$$

mathmale · Answer

or did you mean f(x)=2x-1/3 as in $$f(x)=(2x-1)/3, or f(x)=\frac{ 2x-1 }{ 3 }?$$

shaleiah · Answer

$$f(x)=\frac{ 2x-1 }{ 3}$$

shaleiah · Answer

2x-1=3x

mathmale · Answer

OK.  Fine.  In that case it is essential that y ou enclose "2x-1" inside parentheses, OR write your function as $$f(x)=\frac{ 2x-1 }{ 3 }$$

mathmale · Answer

2x-1=3x ?   Where did that come from?

satellite73 · Answer

close $$2y-1=3x$$ is step one

satellite73 · Answer

next add 1 to both sides

shaleiah · Answer

alright.

mathmale · Answer

Yes, but where did that come from?  Please explain what you're doing.

shaleiah · Answer

2y-1+1=3x+1

mathmale · Answer

Find the inverse of f(x)=2x-1/3.  Note that you MUST write this as f(x)=(2x-1)/3.

Next, replace f(x) with y:  y=(2x-1)/3.

What is the next step, given that you are to find the inverse of f(x)?

satellite73 · Answer

did you get to $$2y=3x+1$$ yet?

shaleiah · Answer

yes

satellite73 · Answer

last step, divide by 2 
which really means just write it

shaleiah · Answer

$$\frac{ 3x+1 }{ 2 }$$

satellite73 · Answer

bingo $$f^{-1}(x)=\frac{3x+1}{2}$$

satellite73 · Answer

notice that $$f(11)=\frac{2\times 11-1}{3}=7$$ and $$f^{-1}(7)=\frac{3\times 7+1}{2}=11$$ just as it should

shaleiah · Answer

Got it :)