Question

given \\(f(x) = 2\sqrt{x}\\) and \\(g(x) = 5x\\), evaluate the following expressions.

(a) \\((f \circ g)(4)\\) (b) \\((g \circ f)(2)\\) (c) \\((f \circ f)(1)\\) (d) \\((g \circ g)(0)\\)

Explanation:

Define the given functions

Using the Composite Functions knowledge point

$$
LATEXBLOCK0
$$

Evaluate part (a)

Using the Composite Functions knowledge point

$$
LATEXBLOCK1
$$

Evaluate part (b)

Using the Composite Functions knowledge point

$$
LATEXBLOCK2
$$

Evaluate part (c)

Using the Composite Functions knowledge point

$$
LATEXBLOCK3
$$

Evaluate part (d)

Using the Composite Functions knowledge point

$$
LATEXBLOCK4
$$

Answer:

Question 1

(a) \((f \circ g)(4) = 4\sqrt{5}\)

Question 2

(b) \((g \circ f)(2) = 10\sqrt{2}\)

Question 3

(c) \((f \circ f)(1) = 2\sqrt{2}\)

Question 4

(d) \((g \circ g)(0) = 0\)