Answer:
g(f(x)) = x
Step-by-step explanation:
You are given f(x) = -4x - 1 and g(x) = [tex]\frac{x+1}{-4}[/tex]. Keep in mind that f(x) or g(x) is the same as a y = equation, but two separate equations.
You are trying to find g(f(x)), which means that you will use f(x) and substitute this value into the x value in the equation of g(x).
It will look like: g(-4x - 1) = [tex]\frac{x+1}{-4}[/tex]
[tex]\frac{(-4x-1)+1}{-4}[/tex]
Now evaluate the expression to solve the problem. Start by combining like terms.
[tex]\frac{(-4x)}{-4}[/tex]
You are left with -4x/-4. We can simplify this even further by dividing both sides of the fraction by -4/-4. The -4's cancel out and become 1's, so you are left with:
[tex]x[/tex]
