Question

What is the inverse of the function f(x) = one-ninthx + 2? h(x) = 18x – 2 h(x) = 9x – 18 h(x) = 9x + 18 h(x) = 18x + 2

Answer 1

h(x) = 9x – 18

Explanation:

y = 1/9 x + 2

To find the inverse, switch x and y and solve for y.

x = 1/9 y + 2

x − 2 = 1/9 y

y = 9x − 18

Answer 2

h(x) = 9x – 18

Explanation:

To find out the Inverse Function consists in discovering a function whose Domain is the Range of the original function, and whose Range is the Domain of the original one.

The procedure is to switch the variables and then isolate again y:

`h(x)=(1)/(9)x+2\Rightarrow y=(1)/(9)x+2\Rightarrow x=(1)/(9)y+2 *(9)\\9x=y+18\Rightarrow -y=18-9x\Rightarrow y=9x-18\Rightarrow h(x)^(-1)=9x-18`

Check the graph, for the green curve the original one and the red one for its inverse.