Given :
- A linear function is given to us .
- The function is h(x) = ⅚x + 1 .
To Find :
- The inverse of the linear function that is h -¹ (x) .
Solution :
Given function to us is : ⅚ x + 1 .
Here is step by step explanation :
Step 1 : Replace h(x) with y .
The equation becomes ,
⇒ y = ⅚x + 1 .
Step 2 : Interchange the variables .
⇒ x = ⅚y + 1.
Step 3 : Solve for y .
⇒x = ⅚ y + 1.
⇒ x - 1 = ⅚y .
⇒ y = 6/5 ( x - 1 )
⇒ y = 6/5x - 6/5 .
Step 4 : Replace y again with [tex]\underline{\sf h^{-1}(x)}[/tex]
⇒ [tex]\bf h^{-1}(x)=\dfrac{6}{5}x-\dfrac{6}{5}[/tex]
[tex]\large\boxed{\red{\bf \purple{\longmapsto}\:h^{-1}(x)\:\:=\:\:\dfrac{6}{5}x-\dfrac{6}{5}}}[/tex]
