Question

if $f(x) = x^2 + x$ and $g(x) = x + 7$, evaluate each of the following.
(a) $(f \circ g)(1)=\square$
(b) $(g \circ f)(1)=\square$
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Explanation:

Part (a)

Step1: Find \( g(1) \)

First, we need to find the value of \( g(x) \) when \( x = 1 \). The function \( g(x)=x + 7 \), so substitute \( x = 1 \) into \( g(x) \):
\( g(1)=1 + 7=8 \)

Step2: Find \( f(g(1)) \)

Now, we need to find \( f(x) \) when \( x = g(1)=8 \). The function \( f(x)=x^{2}+x \), so substitute \( x = 8 \) into \( f(x) \):
\( f(8)=8^{2}+8=64 + 8=72 \)

Step1: Find \( f(1) \)

First, we need to find the value of \( f(x) \) when \( x = 1 \). The function \( f(x)=x^{2}+x \), so substitute \( x = 1 \) into \( f(x) \):
\( f(1)=1^{2}+1=1 + 1=2 \)

Step2: Find \( g(f(1)) \)

Now, we need to find \( g(x) \) when \( x = f(1)=2 \). The function \( g(x)=x + 7 \), so substitute \( x = 2 \) into \( g(x) \):
\( g(2)=2 + 7=9 \)

Answer:

\( 72 \)

Part (b)