Inverse

[rachelmaddie]

Can someone please check my work #15?
To find the inverse of h(x) = (2x + 6)/5, exchange x and y, then solve for y.

h(x) = (2x + 6) /5
y = 2x + 6/5 change to y —> x = (2y + 6)/5
To solve for y, first multiple each side by 5
5x = (2y + 6)/5*5
5x = 2y + 6
Subtract 6 from each side
5x - 6 = 2y + 6-6
5x - 6 = 2y
Divide by 2
(5x - 6)/2 = 2y/2
Therefore, The inverse is (5x - 6)/2

 

[Deleted member 4993]

Can someone please check my work #15?
To find the inverse of h(x) = (2x + 6)/5, exchange x and y, then solve for y.

h(x) = (2x + 6) /5
y = 2x + 6/5 change to y —> x = (2y + 6)/5
To solve for y, first multiple each side by 5
5x = (2y + 6)/5*5
5x = 2y + 6
Subtract 6 from each side
5x - 6 = 2y + 6-6
5x - 6 = 2y
Divide by 2
(5x - 6)/2 = 2y/2
Therefore, The inverse is (5x - 6)/2


View attachment 20298

Your answer is correct.

Thank you for sharing detailed work.

 

[JeffM]

You can check your own work (a clever trick that is helpful on a test)

[MATH]g(x) \text { is the inverse of } f(x) \implies g(f(x)) = x = f(g(x)).[/MATH] ALWAYS.

So

[MATH]h(h^{-1}(x)) = \dfrac{2 * h^{-1}(x) + 6}{5} = \dfrac{\cancel 2 * \dfrac{5x - 6}{\cancel 2} + 6}{5} =\\ \dfrac{5x - 6 + 6}{5} = \dfrac{5x}{5} = x \ \checkmark \\ h^{-1}(h(x)) = \dfrac{\cancel 5 * \dfrac{2x + 6}{\cancel 5} - 6}{2} = \\ \dfrac{2x - 6 + 6}{2} = \dfrac{2x}{x} = x \ \checkmark \checkmark[/MATH]

 

[lookagain]

Can someone please check my work #15?
To find the inverse of h(x) = (2x + 6)/5, exchange x and y, then solve for y.

h(x) = (2x + 6) /5. . . . . . Yes.
y = 2x + 6/5 . . . . . . . . . . No, y = (2x + 6)/5. . . . . And click for the last comment.
change to y —> x = (2y + 6)/5
To solve for y, first multiple each side by 5
5x = (2y + 6)/5*5
5x = 2y + 6
Subtract 6 from each side
5x - 6 = 2y + 6-6
5x - 6 = 2y
Divide by 2
(5x - 6)/2 = 2y/2
Therefore, The inverse is (5x - 6)/2

Continue and write \(\displaystyle \ h^{-1}(x) \ = \ (5x - 6)/2.\)

View attachment 20298

 

[yoscar04]

That was a typo. The problem does say: h(x) = (2x + 6)/5 and not h(x)= 2x + 6/5