Jeanine08181977idn
Answered

IDNLearn.com is designed to help you find reliable answers to any question you have. Find reliable solutions to your questions quickly and easily with help from our experienced experts.

Given [tex]f(x)=x+1[/tex] and [tex]g(x)=x^2[/tex], what is [tex](g \circ f)(x)[/tex]?

[tex]\[
\begin{array}{l}
(g \circ f)(x) = x^2 + x + 1 \\
(g \circ f)(x) = x^2 + 1 \\
(g \circ f)(x) = (x+1)^2 \\
(g \circ f)(x) = x^2(x+1)
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To determine [tex]$(g \circ f)(x)$[/tex], we need to find the composition of the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex].

Given:
[tex]\[ f(x) = x + 1 \][/tex]
[tex]\[ g(x) = x^2 \][/tex]

The notation [tex]\( (g \circ f)(x) \)[/tex] means we apply [tex]\( f \)[/tex] first and then [tex]\( g \)[/tex] to the result of [tex]\( f \)[/tex]. In other words:
[tex]\[ (g \circ f)(x) = g(f(x)) \][/tex]

Step-by-step solution:
1. Start by applying [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) = x + 1 \][/tex]

2. Substitute [tex]\( f(x) \)[/tex] into [tex]\( g(x) \)[/tex]:
[tex]\[ g(f(x)) = g(x + 1) \][/tex]

3. Now substitute [tex]\( x + 1 \)[/tex] into [tex]\( g(x) \)[/tex]:
[tex]\[ g(x + 1) = (x + 1)^2 \][/tex]

Therefore, the composition [tex]\( (g \circ f)(x) \)[/tex] is:
[tex]\[ (g \circ f)(x) = (x + 1)^2 \][/tex]

Among the given options, the correct one is:
[tex]\[ (g \circ f)(x) = (x + 1)^2 \][/tex]
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.