I dont understand my math problems on my algebra 2 homework. can you please help me?

Question

i need help on how to find an equation for the inverse then use compositino to verify that the equation you wrote is the inverse.
problem.#40. h(x)2divided by 3(x-3)+2 and problem #33. g(x)=xdivided by 3

Answer 1

To find the inverse function, let y = h(x) = 2/[3*(x-3)+2]. This can be simplified to y = 2/(3x-7) Interchange x and y to get

x = 2/(3y-7). Solve for y:

x*3(y-7) = 2 3xy - 7x = 2 3xy = 2 + 7x y = (2+7x)/3x; the inverse function is then

h'(x) =(2 + 7x)/3x.

To verify that this is the inverse, put y = h(x) for x in the equation, and the result should come out just x: h'(y) = x is the definition of the inverse function:

h'(y) = (2 + 7y)/3y y is h(x) = 2/(3x-7)

[2+7*(2/(3x-7))//[3*2/(3x-7)] mult top and bottom by 3x-7 to get

(6x-14+14)/6 = x, proving the inverse.

Use the same process for the second part

Answer 2

aaaaaaaaaaaaaah!! thank god i'm done with that shlt!