Question

jika f(x) = 4x - 3 dan g(x) - 2 - 5/x maka (fog)^-1 adalah ?

Answer 1

Pressumed that f(x) = 4x - 3 and g(x) = 2 - 5 / x then

f og(x) = f [g(x)]

Substitute g(x) = 2 - (5 / x) in the above fog(x)

           = f[2 - (5 / x)]

Substitute f(x) = 4x - 3

           = 4(2 - (5 / x)) - 3

           = 8 - (20 / x) - 3

           = 5 - (20 / x)

fog^-1= fog^-1(x) = [fog(x)]^-1

Substitute fog(x) = 5 - (20 / x)

         = [5 - (20 / x) ]^-1

Take out common term 5

         = 5^-1[1 - (4 / x)]^-1

         = 1 / 5[(x - 4) / x]^-1

Recall : Alzebra inverse formula (a / b)^-1 = b / a

         = 1 / 5[x / x - 4].

 

Comments

The inverse function of fog(x) = 5 - (20/x)

y = 5 - (20/x)

To find inverse,

Interchange x and y and solve for y.

x = 5 - (20/y)

x - 5 = - 20/y

y = - 20/(x - 5)

[fog(x)]^-1 = - 20/(x - 5)