Show that f(x)=x^{2}+3x-1 and g(x)=3x^{3}-9x+x-2 are rational functions - that

Walter Clyburn

Walter Clyburn

Answered question

2021-12-13

Show that f(x)=x2+3x1 and g(x)=3x39x+x2 are rational functions - that is, quotients of polynomials.

Answer & Explanation

Dabanka4v

Dabanka4v

Beginner2021-12-14Added 36 answers

Step 1
To show:
That the functions are rational function:
Given:
The functions are f(x)=x2+3x1 and g(x)=3x39x+x2.
Concept used:
The function h(x) is rational function if h(x) is represented as p(x)q(x).
Here, p(x) and q(x) are polynomial function.
Step 2
Verification:
Check first function f(x)=x2+3x1.
f(x)=x2+3×1x
=x3+3x
Therefore, the function f(x)=x2+3x1 can be represented as p(x)q(x), then the function f(x)=x2+3x1 is rational function.
Check first function g(x)=3x39x+x2.
g(x)=3x39x+x2
=3x39x+1x2
=3x59x3+1x2
Therefore, the function g(x)=3x39x+x2 can be represented as p(x)q(x), then the function g(x)=3x39x+x2 is rational function.
Bertha Jordan

Bertha Jordan

Beginner2021-12-15Added 37 answers

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