f(x)=2x+3 g(x)=x^(2)-3x+1 Write g(f(x)) as an expression in terms of x. g(f(x))=

Identify functions: Identify the functions to be composed. We have two functions: f(x) = 2x + 3 g(x) = x^2 - 3x + 1 We need to find the composition of g(f(x)), which means we will substitute f(x) into g(x).Substitute f(x) into g(x): Substitute f(x) into g(x). To find g(f(x)), we replace every instance of x in g(x) with the expression for f(x). So, g(f(x)) = (2x + 3)^2 - 3(2x + 3) + 1Expand (2x + 3)^2: Expand the expression (2x + 3)^2. (2x + 3)^2 = (2x + 3)(2x + 3) = 4x^2 + 6x + 6x + 9 = 4x^2 + 12x + 9Distribute -3: Distribute the -3 across the terms in the parentheses. -3(2x + 3) = -6x - 9Combine terms: Combine all the terms to get the final expression for g(f(x)). g(f(x)) = 4x^2 + 12x + 9 - 6x - 9 + 1Simplify expression: Simplify the expression by combining like terms. g(f(x)) = 4x^2 + (12x - 6x) + (9 - 9 + 1) g(f(x)) = 4x^2 + 6x + 1

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f(x)=2x+3

g(x)=x^(2)-3x+1
Write
g(f(x)) as an expression in terms of
x.

g(f(x))=

$f(x)=2 x+3$ $\newline$ $g(x)=x^{2}-3 x+1$ $\newline$ Write $g(f(x))$ as an expression in terms of $x$ . $\newline$ $g(f(x))=$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

f(x)=2 x+3

\newline

g(x)=x^{2}-3 x+1

\newline

Write

g(f(x))

as an expression in terms of

x

\newline

g(f(x))=

Identify functions: Identify the functions to be composed. $\newline$ We have two functions: $\newline$ $f(x) = 2x + 3$ $\newline$ $g(x) = x^2 - 3x + 1$ $\newline$ We need to find the composition of $g(f(x))$ , which means we will substitute $f(x)$ into $g(x)$ .
Substitute $f(x)$ into $g(x)$ : Substitute $f(x)$ into $g(x)$ . To find $g(f(x))$ , we replace every instance of $x$ in $g(x)$ with the expression for $f(x)$ . So, $g(f(x)) = (2x + 3)^2 - 3(2x + 3) + 1$
Expand $(2x + 3)^2$ : Expand the expression $(2x + 3)^2.$ $(2x + 3)^2 = (2x + 3)(2x + 3) = 4x^2 + 6x + 6x + 9 = 4x^2 + 12x + 9$
Distribute $-3$ : Distribute the $-3$ across the terms in the parentheses. $\newline$ $-3(2x + 3) = -6x - 9$
Combine terms: Combine all the terms to get the final expression for $g(f(x))$ . $g(f(x)) = 4x^2 + 12x + 9 - 6x - 9 + 1$
Simplify expression: Simplify the expression by combining like terms. $\newline$ $g(f(x)) = 4x^2 + (12x - 6x) + (9 - 9 + 1)$ $\newline$ $g(f(x)) = 4x^2 + 6x + 1$