Combining the like-terms, the result of the addition of polynomials f(x) and g(x) is given by:
[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]
How do we add polynomials?
We add polynomials combining the like-terms, that is, adding terms with the same exponent.
In this problem, the polynomials are:
- [tex]f(x) = 3x^{\frac{1}{2}} + 7x^{-\frac{1}{4}} + 8x^{-4}[/tex]
- [tex]g(x) = -\frac{7}{4}x^{\frac{1}{2}} + 12x^{-\frac{1}{4}} - 21x^3[/tex]
Combining the like terms, the addition is given by:
[tex]f(x) + g(x) = \left(3 - \frac{7}{4}\right)x^{\frac{1}{2}} + (7 + 12)x^{-\frac{1}{4}} + 8x^{-4} + 21x^3[/tex]
[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]
More can be learned about addition of polynomials at https://brainly.com/question/9438778
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