Find the function given the equation $(g \circ f)(x) = x + 5$ Let $g(x) = 4x + 1$.

Find $f(x)$, given that the equation $(g \circ f)(x) = x + 5$ is true for all values of $x$.

From my text, it looks like this would be expressed as $g[f(x)]$, but I don't see how you can determine the definition of $f(x)$. Do I need to assume a value of x and work backwards through the problem?
$(g\circ f)(x) = g(f(x))$.

So you know that $g(a) = 4a+1$, no matter what $a$ is. I particular, that means that
$$(g\circ f)(x) = g\bigl(f(x)\bigr) = 4(f(x)) + 1.$$
Now, you want $(g\circ f)(x) = x+5$, so that means that whatever $f(x)$ is, you want
$$4(f(x)) + 1 = x+ 5.$$
Can you figure out what $f(x)$ should be for this to be true?
f(x)= (X+4)/4

This is how I got it:

4(f(x))+1=x+5

4(f(x))+1-1=x+5-1

4(f(x))=x+4

(4(f(x)))/4=(x+4)/4

(f(x))=(x+4)/4
So the x that would make the equation true is (x+4)/4