Question

What is the inverse of function h(x)=(5/2)x+4?h-1(x)=

Answer 1

`h^(-1)(x)=(2)/(5)x-(8)/(5)`

Step-by-step explanation:

The given function is

`h(x)=(5)/(2)x+4`

To find the inverse, we first need to replace h(x) with y, so

`y=(5)/(2)x+4`

Now, we need to interchange x and y

`x=(5)/(2)y+4`

Then, solve the equation for y

`\begin{gathered} x-4=(5)/(2)y+4-4 \\ \\ x-4=(5)/(2)y \\ \\ 2(x-4)=2((5)/(2)y) \\ \\ 2(x-4)=5y \\ \\ (2)/(5)(x-4)=(5y)/(5) \\ \\ (2)/(5)(x-4)=y \\ \\ (2)/(5)x-(2)/(5)(4)=y \\ \\ (2)/(5)x-(8)/(5)=y \end{gathered}`

Finally, replace y with h⁻¹(x). So, the inverse function is

`h^{^(-1)}(x)=(2)/(5)x-(8)/(5)`