Given f(x) = 6x - 4 / 2x + 1 find the inverse function , f ^ - 1 (x) , f ^ - 1 (x) =

(x) = -

let y =

rearrange making x the subject, begin by cross-multiplying

y(2x + 1) = 6x - 4

2xy + y = 6x - 4

collect terms in x together

2xy - 6x = - 4 - y

x(2y - 6) = - (4 + y ) ( divide both sides by (2y - 6) )

x =

change y back to x for inverse

(x) = -

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: