Reciprocal Function Tutor

Reciprocal function tutor is nothing but the inverse function tutor. Before knowing about the inverse function we have to know about the one – to – one function. Let us take the domain as X and range as Y of one to one function f. Thus, the reciprocal function of f has the y domain and X range and is represented as  f-1 (y) = x or f(x) = y.

one to one function

Let see about the reciprocal function with example:

Procedure to find the Reciprocal Function Tutor:

To find the formula of the reciprocal function tutor by following the given procedure:

Step 1: Change the given equation in form of function y = f(x).

Step 2: Solve the given equation for x in terms of y.

Step 3: Inter change the x and y variables and therefore y = f-1(x). Thus function of y is equal to reciprocal function of x.

Example Problems – Reciprocal Function Tutor:

Example 1:

Find the reciprocal of the function f(x) = `(3x - 6)/(3x+5)`.

Solution:

Step 1: Let write the given function as y = `(3x - 6)/(3x+5)`..

Step 2: Solve the function of x in term of y.

y = `(3x - 6)/(3x+5)`.

Multiply the denominator of the fraction 3x + 5 to y.

Now, y (3x + 5) = 3x – 6

3xy + 5y = 3x – 6

5y + 6 = 3x – 3xy

5y + 6 = x (3 - 3y)

Now, we get the value of x = `(5y + 6)/(3-3y)`.

Step 3: Now change the variable x in terms of y and vice versa.

Hence y =  `(5x + 6)/(3-3x)`

Thus the reciprocal of the function f(x) =  `(3x - 6)/(3x+5)`. is given by the reciprocal of function f-1 =  `(5x + 6)/(3-3x)`.

Answer: f-1 =  `(5x + 6)/(3-3x)`.

Example 2:

Find the reciprocal of the function f(x) = 7x – 6.

Solution:

Step 1: Let write the given function as y = 7x – 6.

Step 2: Solve the function of x in term of y.

y = 7x – 6

Add 6 on both sides, we get y + 6 = 7x - 6 +6

y + 6 = 7x

Divide 7 on both sides, we get  `(y +6)/(7)`. =  `(7x)/(7)`.

x = `(y +6)/(7)`

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Step 3: Now change the variable x in terms of y and vice versa.

Hence y =`(x +6)/(7)`.

Thus the reciprocal of the function f(x) = 7x - 6 is given by the reciprocal of function f-1 = `(x +6)/(7)`.

Answer: f-1 = `(x +6)/(7)`.