Question

1.2 homework - graphing functions, composition of functions, and piece - wise fu
score: 30/80 answered: 4/8
question 5
function composition
given the function $f(x)=4x - 5$ and the function $g(x)=9x^{2}+3x + 8$ determine
each of the following.
give your answer as an integer or a simplified fraction.
evaluate $f(g(-4))$ $f(g(-4))=$
evaluate $g(f(-3))$ $g(f(-3))=$
question help: video

Explanation:

Part 1: Evaluate \( f(g(-4)) \)

Step 1: Find \( g(-4) \)

Substitute \( x = -4 \) into \( g(x) = 9x^2 + 3x + 8 \).
\( g(-4) = 9(-4)^2 + 3(-4) + 8 \)
\( = 9(16) - 12 + 8 \)
\( = 144 - 12 + 8 \)
\( = 140 \)

Step 2: Find \( f(g(-4)) = f(140) \)

Substitute \( x = 140 \) into \( f(x) = 4x - 5 \).
\( f(140) = 4(140) - 5 \)
\( = 560 - 5 \)
\( = 555 \)

Part 2: Evaluate \( g(f(-3)) \)

Step 1: Find \( f(-3) \)

Substitute \( x = -3 \) into \( f(x) = 4x - 5 \).
\( f(-3) = 4(-3) - 5 \)
\( = -12 - 5 \)
\( = -17 \)

Step 2: Find \( g(f(-3)) = g(-17) \)

Substitute \( x = -17 \) into \( g(x) = 9x^2 + 3x + 8 \).
\( g(-17) = 9(-17)^2 + 3(-17) + 8 \)
\( = 9(289) - 51 + 8 \)
\( = 2601 - 51 + 8 \)
\( = 2558 \)

Answer:

\( f(g(-4)) = \boldsymbol{555} \)
\( g(f(-3)) = \boldsymbol{2558} \)