How Do You Solve Inverse Functions in Algebra Problems?

[kramer733]

Having trouble with this question. Usually i'd have to see examples first and rep it out but time ran out of class and i guess we couldn't see them. He gaves us tons of notes though but I'm not really sure if I'm doing it right.

Homework Statement

for g(t) = 3t-2, determine each of the following.

(the -1 is an inverse..)
a. g -1 (-2)
b. g -1(a+1) - g -1(a)

Homework Equations

The Attempt at a Solution

Here's what i did with the g -1(-2)

g(t)=3t-2
t=3g(t)-2
(t-2)/3=g(t)
(-2-2)/3 = -4/3

I have no idea how to do the next one though. Well yea i do but it's probably completely wrong.

 

[Office_Shredder]

For the next one, you're taking the difference of two values such that, when you apply g to them, one gives you a value 1 larger than the other. How much does x have to increase by for g(x) to increase by 1?

 

[Architeuthis Dux]

As a scientist, it is important to understand the concepts and principles behind mathematical equations rather than just memorizing steps and formulas. It is great that you have notes from your class, but it is important to also practice solving problems and understanding the steps involved. It is understandable that you may have run out of time in class, but I would suggest seeking help from your teacher or a tutor to go over the examples and practice solving problems.

For the first part of the question, g -1 (-2), you are on the right track. The inverse of a function is essentially switching the x and y values, so instead of g(t), you will have g -1 (t). You correctly rearranged the equation to solve for t, but you should use g -1 (t) instead of g(t) when substituting -2 for t. This will give you the value of g -1 (-2).

For the second part of the question, g -1 (a+1) - g -1 (a), you can use the same concept of switching the x and y values. First, find g -1 (a+1) by substituting a+1 for t in the inverse equation. Then, find g -1 (a) by substituting a for t in the inverse equation. Finally, subtract g -1 (a) from g -1 (a+1) to get your final answer.

Remember to always check your work and make sure your answer makes sense in the context of the problem. Don't be afraid to ask for help or clarification when needed. Keep practicing and you will become more confident in solving algebra problems.