Question

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

a. \\((f \circ g)(x)\\); b. \\((g \circ f)(x)\\), c. \\((f \circ g)(1)\\), d. \\((g \circ f)(1)\\)

a. \\((f \circ g)(x) = \\) (simplify your answer)
b. \\((g \circ f)(x) = \\) (simplify your answer)
c. \\((f \circ g)(1) = \\) (simplify your answer)
d. \\((g \circ f)(1) = \\) (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)(1)

Using the Function Composition knowledge point

$$
LATEXBLOCK2
$$

Evaluate (g o f)(1)

Using the Function Composition knowledge point

$$
LATEXBLOCK3
$$

Answer:

a. \((f \circ g)(x) =\) <blank>\(5x^2 - 6\)</blank>

b. \((g \circ f)(x) =\) <blank>\(5x^2 - 30x + 42\)</blank>

c. \((f \circ g)(1) =\) <blank>\(-1\)</blank>

d. \((g \circ f)(1) =\) <blank>\(17\)</blank>