Question

for (f(x) = 5x - 4) and (g(x) = 2x^2 - 3), find the following functions.

a. ((f \circ g)(x)); b. ((g \circ f)(x)); c. ((f \circ g)(-2)); d. ((g \circ f)(-2))

a. ((f \circ g)(x) = \square) (simplify your answer.)

Explanation:

Define the composition of functions

Using the Function Composition knowledge point

$$ (f \circ g)(x) = f(g(x)) $$

Substitute g(x) into f(x)

Using the Function Composition knowledge point

$$
LATEXBLOCK0
$$

Simplify the expression

Using the Function Composition knowledge point

$$
LATEXBLOCK1
$$

Answer:

For \(f(x) = 5x - 4\) and \(g(x) = 2x^2 - 3\), find the following functions.

a. \((f \circ g)(x) =\) <blank>\(10x^2 - 19\)</blank> (Simplify your answer.)