Question

Find (f•g)(x) when f(x)=sqrt x+3/x and g(x)=sqrt x+3/2x

Answer 1

The expression for (f•g)(x) is √x² + 6x + 9/ 2x²

What is a function?

A function is an expression or rule showing the relationship between a dependent and independent variable.

From the information given we have that;

• f(x) = $\sqrt{\frac{x + 3}{x} }$
• g(x) = $\sqrt{\frac{x + 3}{2x} }$

(f•g)(x) means to multiply both functions;

$\sqrt{\frac{x + 3}{x} } *\sqrt{\frac{x + 3}{2x} }$

Multiply through

$\sqrt{\frac{x^2 + 3x + 3x + 9}{2x^2} }$

Add like terms

$\sqrt{\frac{x^2 + 6x + 9}{2x^2} }$

Thus, the expression for (f•g)(x) is √x² + 6x + 9/ 2x²

Learn more about functions here:

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