Question

Let f(x) = 5x + 12 how do you find `f^-1(x)`?

Answer 1

See explanation for the answer `f^(-1)(x) = ( x - 12 )/5`.

Explanation:

Disambiguation:

If y = f(x), then `x = f^(-1)y`. If the function is bijective for `x in (a, b)`,

then there is `1-1` correspondence between x and y.. The

graphs of both `y = f(x)` and the inverse `x = f^(-1)(y)` are identical,

in the interval.

The equation `y = f^(-1)(x)` is obtained by swapping x and y, in the

inverse relation `x = f^(-1)(y)`.

The graph of `y = f^(-1)(x)` on the same graph sheet will be the

graph of y = f(x) rotated through a right angle, in the clockwise

sense, about the origin.

Here

,`y = f(x) = 5x+12`.. Solving for x,

`x = f^(-1)(y) = ( y - 12 )/5`. Swapping x and y,

`y = f^(-1)(x) = (x-12)/5`