Question

Inverse function of y=(3x-4)^2

Answer 1

answer!!!!

so basically:

To find the inverse function of y = (3x - 4)^2, we need to solve for x in terms of y. The steps are as follows:

1. Start with the given equation: y = (3x - 4)^2.

2. Take the square root of both sides of the equation to undo the squaring: √y = √[(3x - 4)^2].

3. Simplify the right side of the equation: √y = |3x - 4|. Note that we include the absolute value symbol because taking the square root of a squared expression eliminates the negative sign, and we need to consider both the positive and negative solutions.

4. Now, isolate x. Subtract 4 from both sides of the equation: √y - 4 = |3x - 4| - 4.

5. Divide both sides of the equation by 3: (1/3)(√y - 4) = (1/3)|3x - 4| - 4/3.

6. Finally, solve for x by considering two cases for the absolute value:

a. When 3x - 4 is positive, we have: (1/3)(√y - 4) = (1/3)(3x - 4) - 4/3. Simplify this equation to find the value of x.

b. When 3x - 4 is negative, we have: (1/3)(√y - 4) = -[(1/3)(3x - 4) - 4/3]. Simplify this equation to find the value of x.

These two cases will give you the two branches of the inverse function.

Please note that providing the exact values of x may be complicated without a specific value of y. However, by following these steps, you can find the inverse function of y = (3x - 4)^2 and solve for x in terms of y!!!!

hope it helped!! ily!! - aydn

Answer 2

To find the inverse function of y = (3x - 4)^2, we can follow these steps:

1. Start with the given function: y = (3x - 4)^2.

2. Replace y with x and x with y to switch the variables: x = (3y - 4)^2.

3. Take the square root of both sides to isolate the squared term: √x = 3y - 4.

4. Add 4 to both sides to isolate the term with y: √x + 4 = 3y.

5. Divide both sides by 3 to solve for y: y = (1/3)(√x + 4).

Therefore, the inverse function of y = (3x - 4)^2 is given by:

f^(-1)(x) = (1/3)(√x + 4).

This means that if you plug in a value for x into the inverse function, it will give you the corresponding value of y for the original function.

Explanation: