Question

BRAINLIESTTT ASAP! PLEASE HELP ME :) Find the inverse of :

Answer 1

Answer:

$\displaystyle h^{-1}(x) = 2\frac{1}{2}x - 3$

Step-by-step explanation:

$\displaystyle y = \frac{2x + 6}{5} → x = \frac{2y + 6}{5} \\ \\ 5x = 2y + 6$

5x = 2y + 6

- 6 - 6

_________

$\displaystyle \frac{-6 + 5x}{2} = \frac{2y}{2} \\ \\ -3 + 2\frac{1}{2}x = y → h^{-1}(x) = 2\frac{1}{2}x - 3$

I am joyous to assist you anytime.

Answer 2

Answer:

$h^{-1}(x) = \dfrac{5x - 6}{2}$

Step-by-step explanation:

$h(x)= \dfrac{2x + 6}{5}$

(a) Rename h(x) as y  

$y = \dfrac{ 2x+ 6}{5}$

(b) Solve for x :  

$\begin{array}{rcl}y& = &\dfrac{2x + 6}{5}\\\\5y & = & 2x + 6\\5y - 6 & = & 2x\\x & = & \mathbf{\dfrac{5y - 6}{2}}\end{array}$

(d) Switch x and y  

$y = \dfrac{5x -6}{2}$

(e) Rename y as the inverse function  

$h^{-1}(x) = \mathbf{\dfrac{5x - 6}{2}}$

The graphs of inverse functions are reflections of each other across the line y = x.

In the diagram, the graph of h⁻¹(x) is the reflection of h(x) about the line y = x.