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F(x) = 4x + 12, g(x) = x + 2Find the domain of f ∘ g.

F(x) = 4x + 12, g(x) = x + 2Find the domain of f ∘ g.-example-1
User Guinther Kovalski
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1 Answer

22 votes
22 votes
Answer:
Domain:\text{ \lparen-}\infty\text{, }\infty)\text{ \lparen option B\rparen}

Step-by-step explanation:

Given:

f(x) = 4x + 12

g(x) = x + 2

To find:

f ∘ g

To determine f ∘ g, we will substiute x in f(x) with function g(x)


\begin{gathered} f∘g\text{ = \lparen f \circ g\rparen\lparen x\rparen} \\ (f∘g)(x)\text{ = f\lparen g\lparen x\rparen\rparen} \\ \\ f(g(x))\text{ = 4\lparen x + 2\rparen + 12} \\ f(g(x))\text{ = 4x + 8 + 12} \\ f\mleft(g\mleft(x\mright)\mright)\text{ = 4x + 20} \\ \\ f∘g\text{ = 4x + 20} \end{gathered}

Domain are the inputs (x values) of a function

The function f ∘ g = 4x + 20 does not have a restriction on the x values. x can take on any number

Hence, the domain of f ∘ g is all real number


Domain:\text{ \lparen-}\infty\text{, }\infty)\text{ \lparen option B\rparen}

User AaronHolland
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