Find the inverse function of f(x)=x-4/7

Question

mathmale · Answer

Have you found inverse functions before?  if so, what steps did you go through to find the inverse of a given function?

anonymous · Answer

f^−1(x)=4/7+x

anonymous · Answer

inverse function is the opposite of the function

whpalmer4 · Answer

@sensuelle1985 uh, no, that isn't correct.

anonymous · Answer

can you explain why please? @whpalmer4

whpalmer4 · Answer

I was hoping that the original poster would answer my colleague's question...

The way I find inverse functions is by swapping the variables and solving.  As an example, I'll do a problem I just did elsewhere on OS:

$$y = f(x) = \frac{3x-4}{5}$$We swap the variables:
$$x = \frac{3y-4}{5}$$Now solve for $y$:$$5x=3y-4$$$$5x+4=3y$$$$y=f^{-1}(x) = \frac{5x+4}{3}$$

whpalmer4 · Answer

One of the nifty things about finding inverse functions is that they are the same as the original function, except reflected across the line $y = x$:

whpalmer4 · Answer

In that graph, the purple and blue lines are the function and inverse (I don't recall which is which), and the olive line is the line of reflection

anonymous · Answer

Okay got it, thanks for the clarification but is my answer right though?

whpalmer4 · Answer

No, it's not.  Assuming you mean $$f^{-1}(x) = \frac{4}{7} + x$$that's just $y=x$ shifted up by $\large \frac{4}7$, not a reflection of $\large y = \frac{x-4}7$, which is undoubtedly what the poster intended.  Yes, yours is correct if you interpret what they wrote "correctly" but the usual circumstances here are students don't realize that
$$x+4/y$$ does not mean $$\frac{x+4}7$$