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3. Find the composition (fog)(-2) for the functions f(x) = 2x+1 and g(x)=x²-3

3. Find the composition (fog)(-2) for the functions f(x) = 2x+1 and g(x)=x²-3-example-1
User Enigmatic Wang
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1 Answer

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25 votes

Answer:

3

Explanation:

Given functions:


\begin{cases}f(x)=2x+1\\g(x)=x^2-3\end{cases}

Function composition is an operation that takes two functions and produces a third function.

The given composite function f o g(-2) means to substitute the function g(-2) in place of the x in function f(x):


\begin{aligned}(f \circ g)(-2)&=f[g(-2)]\\&=2[g(-2)]+1\\&=2(2^2-3)+1\\&=2(4-3)+1\\&=2(1)+1\\&=2+1\\&=3\end{aligned}

User Richard Vivian
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