Optional callout text right side.

**Note:** This tutorial mainly targets O/L & A/L students.

If f(x) … the inverse function will be f^-1 (x)

Try to understand the theory along with the ‘questions and answers’ – leave a comment if you’re finding it hard to do so, we’ll explain further.

This is going to be more than just a tutorial. Let’s make this a quiz. I will do 4 questions (difficulty-random) along with detailed workings. First try it yourself then check the answer(s). Ok? Great!

Lets assume that **||||** means to-separate, just for our convenience.

**Questions**

1) f(x) = (3x-2)/4

2) g(x) = (x-1)/x, x≠10

3) h(x) = (x+5)/(x-5), x≠5

4) p(x) = √(x-4), x≥4

5) t(x) = 5(2x-3)/2

**Answers**

**1) **f(x) = (3x-2)/4 |||| y = (3x-2)/4

then interchange all “y”s with “x”s : x = (3y-2)/4

now make “y” the subject of the equation again

x = (3y-2)/4

4x = 3y-2

3y = 4x + 2

y = f^-1 (x) = (4x+2)/3

**2)** g(x) = (x-1)/x |||| y = (x-1)/x

x = (y-1)/y

xy = y – 1

xy – y = -1

y(x-1) = -1

y = g^-1 (x) = -1/(x-1) OR 1/(1-x)

**3)** h(x) = (x+5)/(x-5) |||| y = (x+5)/(x-5)

x = (y+5)/(y-5)

x(y-5) = y + 5

xy – 5x = y + 5

xy – y = 5x + 5

y(x-1) = 5x + 5

y = h^-1 (x) = (5x+5)/(x-1)

**4)** p(x) = √(x-4) |||| y = √(x-4)

x = √(y-4)

x^2 = y – 4

y = p^-1 (x) = x^2 + 4

**5)** t(x) = 5(2x-3)/2 |||| y = 5(2x-3)/2

x = 5(2y-3)/2

x = (10y-15)/2

2x = 10y – 15

10y = 2x + 15

y = t^-1 (x) = (2x+15)/10

*– thanks for your comments*

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