Finding Inverse of a function: needing explanation of topic

[Kristen_Opp]

I just started a new chapter and don't know how to get going. I'm taking this class online, I've read the lectures but I wasn't given any examples. If I could just get a totally clear step by step explanation I could maybe apply it and use it as an example for the rest of the problems in the lesson. HELP! ; )

These are the two problem types:

#1) Find the inverse of F(x)= 1/2x-7

(I don't even know how to get started.)

#2) Given (3x - 2)^2 = 17, x > 2/3, solve equation by finding an inverse function.

 

[mark07]

1) To find the inverse function of F, set y=F(x) and solve the equation for x. What you get at the end is simply \(\displaystyle x = F^{-1}(y)\). Changing the name of the variable from y to x, you get the inverse function \(\displaystyle F^{-1}(x)\).

Please use parenthesis to be clear about which function you mean. I assume you meant the following, if not, method is the same but you'll get a different answer.

\(\displaystyle \L y = \frac{1}{2x-7}\)

\(\displaystyle \L y(2x-7) = 1 \Rightarrow 2xy -7y = 1 \Rightarrow 2xy = 7y + 1\)

\(\displaystyle \L x = \frac{7y+1}{2y}\)

\(\displaystyle \L F^{-1}(y) = \frac{7y+1}{2y}\)

or with a change of name from y to x,

\(\displaystyle \L F^{-1}(x) = \frac{7x+1}{2x}\)

 

[mark07]

2) Let's write your equation using a function. Say

\(\displaystyle \L F(x) = (3x-2)^2 \;\;\; \text{for} \;\; x \geq 2/3\).

You want to find x for which \(\displaystyle F(x)=17\). You can find \(\displaystyle F^{-1}\) as I did in the first problem. Then your equation is the same as \(\displaystyle \L x = F^{-1} (17)\) right?

Find \(\displaystyle F^{-1}\) and plug in 17.

 

[stapel]

If I could just get a totally clear step by step explanation...

While we cannot provide the requested lessons within this environment, there are many good lessons available online. Please review a few, and then see if you can follow the worked solution, provided earlier.

Thanky ou.

Eliz.