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 )=x)
and we also use )=x)
. We have to check both equations.
Since we're given that =4x-8)
and you claim that =x+2)
, this means that )=4(x+2)-8=4x+8-8=4x)
which is NOT equal to 'x'. So is not correct.
---------------------------------------------------------
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 =\frac{1}{4}x+2)
---------------------------
Check:
Let's first see if
... Start with the given function.
)=4\left(\frac{1}{4}x+2\right)-8)
... Plug in
)=4\left(\frac{1}{4}x\right)+4\left(2\right)-8)
... Distribute.
)=\frac{4}{4}x+8-8)
... Multiply
)=\frac{4}{4}x)
... Combine like terms.
... Reduce.
Now let's see if
... Start with the inverse function.
)=\frac{1}{4}(4x-8)+2)
... Plug in
)=\frac{1}{4}(4x)+\frac{1}{4}(-8)+2)
... Distribute.
)=\frac{4x}{4}+\frac{-8}{4}+2)
... Multiply
)=x-2+2)
... Reduce
... Combine like terms.
So we've shown that and
So this verifies that the inverse function of is indeed
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