Algebra

Ok, we can go one by one to solve these problems. 

Hoever, let's note that if we have f(x) = x, then we set the right side of the function to equal x.

Then, we see if the x value satisfies the conditions given. 

 

First, we have $f(x) = 2x + 8$. Setting this to equal x, we fuind that $x=2x+8$

Solving for x, we find that $x=-8$. This doesn't satisfy the condition $1 \le x \le 2$, so it is not a valid solution. 

 

Next, we have $f(x) = 13 - 5x$. Setting this to equal x, we have $x=13-5x$

Finding the value of x, we get $x=13/6$. This satisfies the inerval, so it is a solution. 

 

Third, we have $f(x) = 20 - 14x$. Since this equals x, we can write $x = 20 - 14x$ 

Trying to find x, we have that $x=20/15=4/3$. This does NOT satisfy the interval, so it is not a solution. 

 

Lastly, we have $f(x) = 40 + 5x$. setting this function to equal x, we have $x=40+5x$

Solving for x, we get $x=-10$, which is invalid. 

 

Thus, the only value that works i 13/6. 

So our answer is 13/6. 

 

Thanks! :)