Question

homework 16: section 3.4
score: 57.5/160 answered: 6/16
question 6
given that $f(x) = 8x + 1$ and $g(x) = 6 - x^2$, calculate
(a) $f(g(0))=$
(b) $g(f(0))=$

Explanation:

Part (a)

Step1: Calculate \( g(0) \)

Substitute \( x = 0 \) into \( g(x)=6 - x^{2} \).
\( g(0)=6 - 0^{2}=6 \)

Step2: Calculate \( f(g(0)) \)

Substitute \( g(0) = 6 \) into \( f(x)=8x + 1 \).
\( f(6)=8\times6 + 1=48 + 1 = 49 \)

Step1: Calculate \( f(0) \)

Substitute \( x = 0 \) into \( f(x)=8x + 1 \).
\( f(0)=8\times0 + 1=1 \)

Step2: Calculate \( g(f(0)) \)

Substitute \( f(0) = 1 \) into \( g(x)=6 - x^{2} \).
\( g(1)=6 - 1^{2}=6 - 1 = 5 \)

Answer:

\( 49 \)

Part (b)