Questions: If f(x)=x^2-19 and g(x)=4x^3-3x^2+8, find f(x)-g(x)

Transcript text: If \( f(x)=x^{2}-19 \) and \( g(x)=4 x^{3}-3 x^{2}+8 \), find \( f(x)-g(x) \)

Solution

Step 1: Define the Functions

We start by defining the functions given in the problem: \[ f(x) = x^2 - 19 \] \[ g(x) = 4x^3 - 3x^2 + 8 \]

Step 2: Calculate \( f(x) - g(x) \)

Next, we compute the difference between the two functions: \[ f(x) - g(x) = (x^2 - 19) - (4x^3 - 3x^2 + 8) \]

Step 3: Simplify the Expression

We simplify the expression obtained in the previous step: \[ f(x) - g(x) = -4x^3 + 4x^2 - 27 \]

\(\boxed{-4x^3 + 4x^2 - 27}\)

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