Question

if (x)=12 x+7, what is f^1 (x)

Answer 1

check is it's f^1(x) or f^-1(x)?

Answer 2

Are you looking for a derivative?

f^1(x), by exponent rule, will be f^1(x) = 12

Answer 3

this says multiply by 12, add 7
inverse say subtract 7, divide by 12
it is
\[f^{-1}(x)=\frac{x-7}{12}\]

Answer 4

if you like you can write
\[y=12x+7\] switch x and y which is what the inverse does and write
\[x=12y+7\] solve for y get
\[x-7=12y\]
\[\frac{x-7}{12}=y\] so
\[f^{-1}(x)=\frac{x-7}{12}\] that way