h(x)= 3x+2/7x-6

Question

find the inverse of h^-1(x)

h^-1(x) = ?

Would I solve it like this

h(x)= 3x+2/7x-6

7xy-6y=3x+2 (bring 7x-6 to other side)

i got confused here. Would i try to bring the 6y over to the right and then the 3x+2 to the left to get Y by itself. then solve ?

Answer 1

Brackets are essential here ....

h(x) = (3x+2)/(7x-6) or
y = (3x+2)/(7x-6)

step 1 of finding the inverse is to interchange the x's and y's
x = (3y + 2)/(7y - 6)
7xy - 6x = 3y + 2

step 2 : solve this for y

7xy - 3y = 6x + 2
y(7x - 3) = 6x + 2
y = (6x + 2)/(7x - 3) , brackets needed here again.

h^-1 (x) = (6x + 2)/(7x - 3)

checking for any value of x, say x = 1
then h(1) = (3+2)/(7-6) = 5
h^1 (5) = (30+2)/(35-3)
= 32/32 = 1
Yeahhh , it is highly probable that my answer is correct

Answer 2

Find the inverse function for h(x)=6x^2+4 and g(x)=7x/6