Question

What is the inverse of the function h(x) = 3 over 4 x+12

Answer 1

To answer this question we will set the equation y=f(x), then we will solve the equation for x, and finally, we will exchange x and y.

Setting y=f(x) we get:

`y=(3)/(4)x+12.`

Subtracting 12 from the above equation we get:

`\begin{gathered} y-12=(3)/(4)x+12-12, \\ y-12=(3)/(4)x\text{.} \end{gathered}`

Multiplying the above equation by 4/3 we get:

`\begin{gathered} (y-12)*(4)/(3)=(3)/(4)x*(4)/(3), \\ x=(4)/(3)y-16. \end{gathered}`

Exchanging x and y in the above equation we get:

`y=(4)/(3)x-16.`

Therefore the inverse function of h(x) is:

`h^(-1)(x)=(4)/(3)x-16.`

Answer:

`h^(-1)(x)=(4)/(3)x-16.`