Question

Find the inverse function of

f(x)=20x-4

Domain of f(x)

Domain of f^-1(x)

Range of f(x)

Range of f^-1(x)

help can you show work for question please

Answer 1

`f(x) = 20x - 4 \\ substitute \: y \: for \: f(x) \\ y = 20x - 4 \\ interchange \: x \: and \: y \\ x = 20y - 4 \\ swap \: the \: sides \: of \: the \: equation \\ 20y - 4 = x \\ move \: the \: constant \: to \: the \: right \: hand \\ 20y = x + 4 \\ divide \: both \: sides \: by \: 20 \\ y = (1)/(20) x + (1)/(5) \\ substitute \: f {}^( - 1) (x) \: for \: y \\ f {}^( - 1) (x) = (1)/(20) x + (1)/(5)`

The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.

Thus, domain of f(x): x∈R = range of f¯¹(x)

and range of f(x): x∈R =domain of f¯¹(x)