If f(x)= 5x4+10 and g(x) = \sqrt{x} , then for x ≠ 0, the value of f/g (x)= is
Question 14 Answer
a.

5x7/2 + 10x-1/2

b.

5x7/2 + 10x1/2
c.
5x9/2 +10 \sqrt{x}
d.

5x9/2 +5 \sqrt{x}

We are tasked with finding \( \frac{f(x)}{g(x)} \), where:

\[
f(x) = 5x^4 + 10
\]
\[
g(x) = \sqrt{x} = x^{1/2}
\]

The expression for \( \frac{f(x)}{g(x)} \) is:

\[
\frac{f(x)}{g(x)} = \frac{5x^4 + 10}{x^{1/2}}
\]

Now, let's simplify each term separately by dividing by \( x^{1/2} \):

\[
\frac{5x^4}{x^{1/2}} = 5x^{4 - 1/2} = 5x^{7/2}
\]

\[
\frac{10}{x^{1/2}} = 10x^{-1/2}
\]

Thus, the expression becomes:

\[
\frac{f(x)}{g(x)} = 5x^{7/2} + 10x^{-1/2}
\]

This matches **option a**:

\[
\boxed{5x^{7/2} + 10x^{-1/2}}
\]

Would you like further details or explanations on any part of this solution?

Here are 5 related questions for further exploration:
1. How do you simplify expressions involving fractional exponents?
2. What are the properties of functions involving square roots?
3. How do you divide polynomials by monomials?
4. What are the rules for exponents when adding or subtracting powers?
5. How do you find the domain of a function involving square roots?

**Tip:** When dividing terms with the same base, subtract the exponents!

If f(x)= 5x^4 + 10 and g(x) = √x, then for x ≠ 0, the value of f/g(x) is?

Explore how to simplify the rational expression f(x)/g(x) where f(x) = 5x^4 + 10 and g(x) = √x. This problem covers exponents, algebra, and the laws of exponents, suitable for high school students in Grades 10-12.

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