Question

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

Answer 1

Answer:

$h^{-1}(x)=\frac{2}{5}x-\frac{8}{5}$

Explanation:

The given function is

$h(x)=\frac{5}{2}x+4$

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

$y=\frac{5}{2}x+4$

Now, we need to interchange x and y

$x=\frac{5}{2}y+4$

Then, solve the equation for y

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

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

$h^{^{-1}}(x)=\frac{2}{5}x-\frac{8}{5}$