For f left parenthesis x right parenthesis equals 5 x plus 7 and g left parenthesis x right parenthesis equals x squared comma find the following composite functions and state the domain of each.
​(a)  fcircleg         ​ (b)  gcirclef           ​ (c)  fcirclef            ​ (d)  gcircleg

Given the functions \( f(x) = 5x + 7 \) and \( g(x) = x^2 \), let's solve the composite functions and determine the domains of each.

### (a) \( f \circ g \) (this means \( f(g(x)) \))

\[
f(g(x)) = f(x^2) = 5(x^2) + 7 = 5x^2 + 7
\]

- **Domain**: Since \( g(x) = x^2 \) is a polynomial, and the function \( f(x) = 5x^2 + 7 \) is also a polynomial, the domain is all real numbers: \(

For f(x) = 5x + 7 and g(x) = x^2, find the following composite functions and state the domain of each: (a) f ∘ g (b) g ∘ f (c) f ∘ f (d) g ∘ g.

Explore how to solve composite functions f ∘ g, g ∘ f, f ∘ f, and g ∘ g for the functions f(x) = 5x + 7 and g(x) = x^2. This guide provides detailed solutions and domain analysis for each composite function. Suitable for students in Grades 9-12.

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Solution

(a) $f \circ g$ (this means $f(g(x))$ )

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