Question

w2a2: compositions of functions assignment
score: 0/100 answered: 0/7
question 1
given that $f(x) = 7x - 1$ and $g(x) = 3$, calculate
(a) $f(g(-9))$ =
(d) $g(f(0))$ =
question help: video 1 video 2

Explanation:

Part (a): Calculate \( f(g(-9)) \)

Step 1: Find \( g(-9) \)

The function \( g(x) = 3 \) is a constant function, so for any input \( x \), \( g(x) = 3 \). Thus, \( g(-9) = 3 \).

Step 2: Substitute into \( f(x) \)

Now we need to find \( f(g(-9)) = f(3) \). The function \( f(x) = 7x - 1 \), so substitute \( x = 3 \) into \( f(x) \):
\( f(3) = 7(3) - 1 = 21 - 1 = 20 \).

Part (d): Calculate \( g(f(0)) \)

Step 1: Find \( f(0) \)

Substitute \( x = 0 \) into \( f(x) = 7x - 1 \):
\( f(0) = 7(0) - 1 = 0 - 1 = -1 \).

Step 2: Substitute into \( g(x) \)

The function \( g(x) = 3 \) is constant, so \( g(f(0)) = g(-1) = 3 \).

Answer:

s:
(a) \( \boldsymbol{20} \)
(d) \( \boldsymbol{3} \)