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Weird Algebra 1 problem


QuantumPerihelion

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So suppose f(x) = 4x - 5. Solve f(f(x)) = 23 for x.

 

I have no idea how to solve what I think is a function of a function, as I am new to this type of "basic" algebra problem.

 

Not a homework problem just trying to learn new things from some things I found online.

Edited by QuantumPerihelion
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So suppose f(x) = 4x - 5. Solve f(f(x)) = 23 for x.

 

I have no idea how to solve what I think is a function of a function, as I am new to this type of "basic" algebra problem.

 

Not a homework problem just trying to learn new things from some things I found online.

So, if f(x) = 4x - 5, then f(g) = 4g - 5.

 

Now, substitute in f(x) for g. Can you get it from there?

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  • 2 weeks later...

It is a composition problem you put f(x) in for x. So with your equation you would have 4(4x-5)-5=23
If that makes sense don't read further.

The idea of a composition function is to place a function inside of another function.
Common function names used are f(x) and g(x) however this does not have to be you can have other names such as h(x)
There are two ways to tell a composition function f(g(x)) or f(x)○g(x)
So say you have your problem, lets split it up into two separate functions f and g.
f(x) = 4x-5 and g(x) = 4x-5

We take the function f(x) and replace all x's with g(x) and set it equal to 23 like such.

4(g(x)) - 5 = 23

Now we plug in g(x)

4(4x - 5) - 5 = 23
and begin to solve
16x - 20 - 5 = 23
16x - 25 = 23
16x = 48

x = 3

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Rather than actually finding f(f(x)) you can do it this way: let y= f(x) so that f(f(x)) is f(y)= 4y- 5= 23. Solving that, 4y= 23+ 5= 28 so y= 28/4= 7. So now y= f(x) becomes 7= 4x- 5. Again, 4x= 7+ 5= 12, x= 12/4= 3. Check: f(3)= 4(3)- 5= 12- 5= 7 so that f(f(3))= 4(7)- 5= 28- 5= 23.

Edited by Country Boy
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