Question

Determine the inverse of the given function
f(x)= 2x-9/4​

Answer 1

Inverse of a Function

To find the inverse of a function:

1. Replace f(x) with y
2. Switch around x and y
3. Isolate y
4. Replace y with f⁻¹(x)

Solving the Question

`f(x)= 2x-(9)/(4)`

⇒ Replace f(x) with y:

`y= 2x-(9)/(4)`

⇒ Switch around y and x:

`x= 2y-(9)/(4)`

⇒ Isolate y:

`x+(9)/(4)= 2y\\\\(1)/(2)(x+(9)/(4))= 2y((1)/(2))\\\\(1)/(2)x+((1)/(2)*(9)/(4))= y\\\\(1)/(2)x+(9)/(8)= y\\\\y=(1)/(2)x+(9)/(8)`

⇒ Replace y with f⁻¹(x):

`f^(-1)(x)=(1)/(2)x+(9)/(8)`

Answer

`f^(-1)(x)=(1)/(2)x+(9)/(8)`