Question

PRE-CALCULUS • INVERSE FUNCTIONS
If f(x) = 6 − 7x, find f ^−1(−57).

(You can just tell me how to do it without actually going through the steps/checking my work. I understand the limitations imposed by the CoC; it's only fair after all.)

Answer 1

more legible:\[\text{if }f(x)=6-7x,\text{ find }f^{-1}(-57)\]

Answer 2

Hrm, seems the site is glitching. It took me five minutes to get back on here after getting mysteriously "booted" from my own thread. :\

Answer 3

Altho there are other ways in which to do this problem, I'd suggst you yourself actually do the work of finding the inverse of f(x).

1. Replace f(x) with y.
2. Interchange x and y.
3. Solve for y
4. Replace y with \[f ^{-1}(x)\]

Then let x=-57.

Answer 4

Oh, that's how you do it?
Ok, thanks @mathmale

Answer 5

My pleasure.

Answer 6

So then...\[x=6-7y\rightarrow 7y=6-x\rightarrow y=\frac{6}{7}-\frac{1}{7}x\]Is this right? :o\[\text{alternate form }y=-\frac{1}{7}x+\frac{6}{7}\]@mathmale

Answer 7

oops sorry - @mathmale

Answer 8

this alternate form is actually the inverse of f(x) = 6 -7x

now, all you need to do is plug in -57 into your alternate form, which is actually the inverse.

Answer 9

Yep @TheSmartOne I got it, thank you (and to mathmale as well), it really helped ☺ However, I ran into an issue while applying this method to another problem - \[f(x)=\frac{9x-1}{x-2}\]\[x=\frac{9y-1}{y-2}\rightarrow x(y-2)=9y-1\rightarrow xy-2x=9y-1\rightarrow -2x=9y-xy-1\]\[-2x+1=9y-xy\rightarrow -2x+1=y(9-x)\rightarrow -\frac{2x+1}{9-x}=y\]FYI, I ran this answer through several sites to check (Mathway, Cymath, WolframAlpha) and got the same result, yet the site is telling me I got it wrong. :(

Answer 10

PROOF: http://prntscr.com/a557of