Question

What is (f−g)(x)? f(x)=5x^4+4x^3+3x^2+2x+1 g(x)=x^4+2x^3+3x^2+4x+5. Enter your answer, in standard form, in the box.

Answer 1

Answer:

$(f-g)(x)=4x^{4}+2x^3}-2x-4$

Step-by-step explanation:

Let f and g be two functions that are defined in the same interval and have the same independent variable. Then, the Subtraction of Function is defined as:

$(f-g)(x)=f(x)-g(x)$

Let's solve (f-g)(x) with $f(x)=5x^{4}+4x^3}+3x^{2}+2x+1$ and $g(x)=x^{4}+2x^{3}+3x^{2}+4x+5$

$(f-g)(x)=(5x^{4}+4x^3}+3x^{2}+2x+1)-(x^{4}+2x^{3}+3x^{2}+4x+5)\\(f-g)(x)=5x^{4}+4x^3}+3x^{2}+2x+1-x^{4}-2x^{3}-3x^{2}-4x-5\\(f-g)(x)=4x^{4}+2x^3}-2x-4$

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