h(x)= 3x+2/7x-6
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 ?
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
Find the inverse function for h(x)=6x^2+4 and g(x)=7x/6
To find the inverse of the function h(x), you need to swap the roles of x and y and solve for y.
Starting with the original function:
h(x) = (3x + 2)/(7x - 6)
Swap x and y:
x = (3y + 2)/(7y - 6)
Now solve for y:
7xy - 6x = 3y + 2 (multiply both sides by 7y - 6 to eliminate the denominator)
7xy - 6x - 3y = 2 (rearrange terms)
-6x - 3y = -7xy + 2 (move -7xy to the left side)
-3y + 7xy = -6x + 2 (rearrange terms)
Now factor y out on the left side:
y(-3 + 7x) = -6x + 2 (factor out y)
y = (-6x + 2)/(-3 + 7x)
Therefore, the inverse function h^(-1)(x) is:
h^(-1)(x) = (-6x + 2)/(-3 + 7x)
To find the inverse of a function, you need to switch the roles of x and y and solve for y. Here's how you can find the inverse of h(x):
Step 1: Replace h(x) with y to get the equation:
y = (3x + 2) / (7x - 6)
Step 2: Swap the positions of x and y:
x = (3y + 2) / (7y - 6)
Step 3: Solve the equation for y, which means isolating y on one side of the equation:
Multiply both sides of the equation by (7y - 6) to remove the denominator:
x(7y - 6) = 3y + 2
Distribute x to both terms on the left side:
7xy - 6x = 3y + 2
Step 4: Move all terms with y to one side and all constant terms to the other side:
7xy - 3y = 6x + 2
Factor out y on the left side:
y(7x - 3) = 6x + 2
Step 5: Divide both sides of the equation by (7x - 3) to solve for y:
y = (6x + 2) / (7x - 3)
So the inverse function of h(x) is:
h^-1(x) = (6x + 2) / (7x - 3)