Given f(x) = the quantity of x plus 7, divided by 5, solve for f-1(3).

Question

the_fizicx99 · Answer

Inverse function xD

Start by replacing $\ \sf f(x)$ with $\ \sf y$

$\ \sf f(x) = \dfrac{x + 7}{5} \rightarrow y =  \dfrac{x + 7}{5}  $

Now $\ \sf exchange $ y with your x so $\ \sf y =  \dfrac{x + 7}{5}  $ becomes $\ \sf x =  \dfrac{y + 7}{5}  $ and now you want to solve for y. Multiply both sides by 5 and subtract 7 from both sides.

$\ \sf x =  \dfrac{y + 7}{5} \longrightarrow x * 5 ~ or ~ 5x$ 

$\ \sf x =  \dfrac{y + 7}{5} \longrightarrow 5x - 7 = y$ 

Now Simply repleace y with f(x)$^{-1}$

$\ \sf \Large 5x - 7 = y \longrightarrow 5x - 7 = f(x)^{-1} $

Now plug in 3 for x.

the_fizicx99 · Answer

$\ \sf \Large f(\color{orange}{x})^{-1} = 5\color{orange}{x} - 7 $

$\ \sf \color{orange}{x = 3} $

$\ \sf \Large f(\color{orange}{3})^{-1} = 5(\color{orange}{3}) - 7 \rightarrow 15 - 7 = 8$

f(3)^-1 = 8

anonymous · Answer

@Kimberly_PR