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) = 10x^2 - 19\\) (simplify your answer.)
b. \\((g \circ f)(x) = \\) (simplify your answer.)

Explanation:

Find the composition (f o g)(x)

Using the Function Composition knowledge point

$$
LATEXBLOCK0
$$

Find the composition (g o f)(x)

Using the Function Composition knowledge point

$$
LATEXBLOCK1
$$

Evaluate (f o g)(-2)

Using the Function Composition knowledge point

$$
LATEXBLOCK2
$$

Evaluate (g o f)(-2)

Using the Function Composition knowledge point

$$
LATEXBLOCK3
$$

Answer:

Question 1

\((f \circ g)(x) = 10x^2 - 19\)

Question 2

\((g \circ f)(x) = 50x^2 - 80x + 29\)

Question 3

\((f \circ g)(-2) = 21\)

Question 4

\((g \circ f)(-2) = 389\)