Inverse Functions [Mathematics]

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

• AL
• Inverse functions
• Math
• mathematics
• OL