given f(x) = (2x-2)/4 solver for f^1(3)

Question

anonymous · Answer

:/

anonymous · Answer

@amistre64 @phi @jim_thompson5910 @cwrw238

amistre64 · Answer

when y=3, what does x have to be?

or, for what value of x, does f(x) = 3

amistre64 · Answer

$$f(x)=3$$
$$f^{-1}(f(x))=f^{-1}(3)$$
$$x=f^{-1}(3)$$

anonymous · Answer

I know that.... Solving it is my issue because I can't just plug it in

amistre64 · Answer

sure you can, i just demonstarted that f(x) = 3

amistre64 · Answer

f(x) = (2x-2)/4 

3 = (2x-2)/4

amistre64 · Answer

the value of x is equal to f^-1(3)

amistre64 · Answer

even if we dont go that route, but replace x by f^-1(3)
$$f(x)=\frac{2x-2}{4}$$
$$f(f^{-1}(3))=\frac{2(f^{-1}(3))-2}{4}$$
$$3=\frac{2(f^{-1}(3))-2}{4}$$
solve for f^(-1)(3)

anonymous · Answer

If I plug it in, I get 1.
i don't know what the ^-1 means

amistre64 · Answer

^-1 is inverse notation ....

anonymous · Answer

I know that

amistre64 · Answer

youre giving me mixed results here ... you either know or you dont; it cant be both :/

anonymous · Answer

Let me rephrase. I KNOW what the ^-1 IS but I don't know what to do with it

amistre64 · Answer

hmm, you recall that y = f(x)  right?

anonymous · Answer

yep, sorry for the miscommunication

amistre64 · Answer

to undo the f, we apply its inverse;  so f^-1 each side

$$y=f(x)$$
$$f^{-1}(y)=f^{-1}(f(x))$$
$$f^{-1}(y)=x$$
letting y = 3
$$f^{-1}(3)=x$$
and since y = f(x), let f(x) = 3 and solve for x

amistre64 · Answer

hmm, you recall that y = f(x)  right?

anonymous · Answer

so the Y actually equals 3? Although I don't have a Y? Seems weird that they'd give me that

amistre64 · Answer

f(x) is a curve in the xy plane;  for some value of x, we can measure the value of the curve, and relate it to the y axis.

phi · Answer

you could think like this
f(x)  is a rule that changes x into y  

the inverse goes the other way, given y, you find x

amistre64 · Answer

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