Final answer:
The composition of the functions f(g(x)), with f(x) being 2x² and g(x) being √(5x³), simplifies to 10x³. This is a result of substituting g(x) into f(x) and applying the properties of exponents. Option c is the correct answer.
Step-by-step explanation:
When combining functions in mathematics, one of the operations we might perform is function composition. This involves applying one function to the results of another. In this particular case, we are asked to find f(g(x)), where f(x) = 2x² and g(x) = √(5x³). Function composition here means that we will substitute g(x) into f(x), thus evaluating f at the value of g(x).
First, let's express g(x) with a fractional exponent: √(5x³) can be written as (5x³)¹⁄₂. When we then insert g(x) into f(x), we get f(g(x)) = 2((5x³)¹⁄₂)². Applying the exponent of 2 to the inside expression, (5x³)¹⁄₂ becomes 5x³ because the exponent ¹⁄₂ and the exponent 2 cancel each other out. Consequently, the result is f(g(x)) = 2 × 5x³, which simplifies to 10x³.