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

Question

Julia Adams · Accepted Answer

undefined To find the inverse of the function $ f(x) = 5x + 12 $, we switch the roles of $ x $ and $ y $ and solve for $ y $:

$$ y = 5x + 12 $$
$$ x = 5y + 12 $$

Then, solve for $ y $:

$$ x - 12 = 5y $$
$$ \frac{x - 12}{5} = y $$

So, the inverse function is $ f^{-1}(x) = \frac{x - 12}{5} $.

Hazel Anglin · Answer

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

Clarification: 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, during the break. 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 The graph of y = f(x) rotated clockwise at a right angle sense, regarding the source. 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#