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

Question

Answer 1

## Step 1: Analyze the Composite Function### The given composite function

suggests that the inner function

is likely related to the expression

. The outer function

then operates on the result of

. We can see that the outer function squares the output of

, multiplies it by 4, and then adds 1.## Step 2: Define f(x)### Let

. This corresponds to the inner expression within the composite function.## Step 3: Define g(x)### Let

. This corresponds to the operations performed on the output of

.## Step 4: Verify the Composite Function### Substitute

into

:

. This matches the given composite function, confirming our choices for

and

.

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