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

1 Answer
Aug 28, 2016

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#