Question

Let f(x) = 5x + 12. Find f^–1(x).
Help I don't understand how to do this:(

Answer 1

suppose you wanted to solve
\[5x+12=10\] what would you do?

Answer 2

\[5x+12=10\]
1) subtract 12
\[5x=-2\]
2) divide by 5
\[x=-\frac{2}{5}\]
so in other words if you know the output is 10, you know x must have been
\[-\frac{2}{5}\] this is how the inverse works. it tells you what the input is if you know the output

Answer 3

so the inverse says
1) subtract 12
2) divide by 5
and we can write
\[f^{-1}(x)=\frac{x-12}{5}\]

Answer 4

another (identical) way to think about it is this.
\[f(x)=5x+12\] says
1) multiply by 5,
2) add 12

inverse will do the reverse operations in reverse order, so again it is
1) subtract 12
2) divide by 5

Answer 5

okay, thank you:)

Answer 6

and finally (they way you might have seen) is take
\[y=5x+12\] switch x and y to write
\[x=5y+12\] solve for y and get
\[x-12=5y\]
\[\frac{x-12}{5}+y\] and so
\[f^{-1}(x)=y=\frac{x-12}{5}\]

Answer 7

beat that one to death, huh?

Answer 8

haha yes, thank you! I needed it:))