Weird Algebra 1 problem

[QuantumPerihelion]

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 January 24, 2017 by QuantumPerihelion

[ydoaPs]

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?

[QuantumPerihelion]

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

 

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

So then after a few steps 16x - 25 = 23

 

16x = 48

 

x = 3

[ydoaPs]

So then after a few steps 16x - 25 = 23

 

16x = 48

 

x = 3

Great job. Do you have any other problems you need help with?

[mrgriffxy]

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

[Country Boy]

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 February 8, 2017 by Country Boy