If f(x)= 1/1-x
Find the composition of f(f(x)).
So I get 1/1-(1/1-x)
I'm not sure if I am putting it in my calculator correctly because I keep getting a line. Is that right? If I put it in with the parentheses differently, I get the graph of f(x)=1/x.
Does anyone know which graph is right? Thanks in advance.
How in the world can we know which problem is right? Frankly, if I were betting,
f(x)=1/(1-x)
so f(x)=1/(1-1/(1-x))
= (1-x)/(1-x-1)=(1-x)/(-x)= (x-1)/x
check that, it is easy to make an error typing these.
It wouldn't be 1/1-(1/1-x)...it would be 1/1 * (1/1-x)
To find the composition of f(f(x)), we substitute f(x) into f(x) itself. Let's start by plugging in f(x) into the original function:
f(f(x)) = 1 / (1 - f(x))
Now, we need to substitute f(x) into the equation:
f(f(x)) = 1 / (1 - (1 / (1 - x)))
To simplify this expression correctly, we need to be careful with the order of operations and use parentheses correctly. Here's the correct way to simplify it:
f(f(x)) = 1 / (1 - (1 / (1 - x)))
The graph of the function f(x) = 1 / (1 - x) is different from the graph of f(x) = 1 / x. To distinguish between the two, it's essential to use parentheses correctly when entering the expression into a calculator.
Make sure you enclose the entire numerator and denominator of the fraction in parentheses when using a calculator. The correct input should be:
1 / (1 - (1 / (1 - x)))
By entering the expression like this, you should get the correct result without a line.