SOLUTION: I have 20 algebra problems, some of which are to "simplify," "solve," and to "evaluate." What I need is a way to double check my work. Here are a couple of examples; find inverse f

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Question 323243: I have 20 algebra problems, some of which are to "simplify," "solve," and to "evaluate." What I need is a way to double check my work. Here are a couple of examples; find inverse funtion of (x), f(x)=4x-8, my answer is f, raised to the negative 1 power(x)= x+2
Another problem is find inverse of, g(x)=7 raised to the "x" power, my answer is g raised to the negative 1 power(x)= the 7th root of x.
Another example is to evaluate; 3 natural log (e cubed) my answer is 9.
Any feedback would be greatly appreciated. Thank you for your time.
Margie
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
To check if a function is the inverse of another function, we use the property and we also use . We have to check both equations.

Since we're given that and you claim that , this means that which is NOT equal to 'x'. So is not correct.

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Let's find the inverse of

Start with the given function.

Replace f(x) with y

Swap x and y. The goal now is to solve for y

Add 8 to both sides.

Divide both sides by 4 to isolate y.

Rearrange the equation

Break up the fraction

Reduce and simplify.

So the inverse function of is

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Check:

Let's first see if

... Start with the given function.

... Plug in

... Distribute.

... Multiply

... Combine like terms.

... Reduce.

Now let's see if

... Start with the inverse function.

... Plug in

... Distribute.

... Multiply

... Reduce

... Combine like terms.

So we've shown that and

So this verifies that the inverse function of is indeed