4. Find two functions, f(x) and g(x) such that g(f(x))=4(x-1)^2+1 f(x)=underline (x-1),g(x)=4x^2+1

## Step 1: Analyze the Composite Function<br />### The given composite function $g(f(x)) = 4(x-1)^2 + 1$ suggests that the inner function $f(x)$ is likely related to the expression $(x-1)$. The outer function $g(x)$ then operates on the result of $f(x)$. We can see that the outer function squares the output of $f(x)$, multiplies it by 4, and then adds 1.<br /><br />## Step 2: Define f(x)<br />### Let $f(x) = x - 1$. This corresponds to the inner expression within the composite function.<br /><br />## Step 3: Define g(x)<br />### Let $g(x) = 4x^2 + 1$. This corresponds to the operations performed on the output of $f(x)$.<br /><br />## Step 4: Verify the Composite Function<br />### Substitute $f(x)$ into $g(x)$: $g(f(x)) = g(x-1) = 4(x-1)^2 + 1$. This matches the given composite function, confirming our choices for $f(x)$ and $g(x)$.