Question

Given the function f(x) = 6(x+2) − 3, solve for the inverse function when x = 21.

−45

0

2

63

Answer 1

\[\large f(x) = 6(x + 2) - 3\]

First we need to switch the 'x' and y'

\[\large x = 6(y + 2) - 3\]

Now we just solve for 'y' again

\[\large x = 6y + 12 - 3\]

\[\large x = 6y + 9\]

\[\large 6y = x - 9\]

\[\large y = \frac{x - 9}{6}\]

That is our inverse

\[\large f(x) = 6(x + 2) - 3\]
\[\large f^{-1}(x) = \frac{x - 9}{6}\]

Now just plug in 21 for 'x' and solve for 'y'

Answer 2

i never understood the wording of these questions although i see them all the time here

"solve for the inverse function when x = 21. "

Answer 3

^Indeed, the wording is terrible, but it always seems to be the same thing they are asking

Answer 4

i can only assume it means find
\[f^{-1}(21)\] which translates as "solve for \(x\) \[\large 6(x+2) − 3=21\]

Answer 5

Ha what do you know it comes out to the same answer

Answer 6

add 3
divide by 6
subtract 2