How do you find the compositions given $F (x) = x + 4$ $F(x)=x+4$ and $g (x) = x^{2}$ $g(x)=x^2$ ?

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How do you find the compositions given $F (x) = x + 4$ $F(x)=x+4$ and $g (x) = x^{2}$ $g(x)=x^2$ ?

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Answer 1 · 2016-01-03T17:07:22

The composition of two functions is really just substituting one function as the x value of the other. See example below for detailed explanation.

Explanation:

Example 1: Find ƒ(g(2))

This means that what would be ƒ's y value when g's x value is 2. We find this by substituting 2 for x in g(x) and then putting the solution to that into ƒ(x).

ƒ(g(2)) = ƒ( $2^{2}$ $2^2$ )

= ƒ(4) = 4 + 4

ƒ(g(2)) = 8

Example 2: Find g(ƒ(x))

= g(x + 4)
= ${(x + 4)}^{2}$ $(x + 4)^2$
= $x^{2}$ $x^2$ + 8x + 16

Hopefully you understand now

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How do you find the compositions given $F (x) = x + 4$ $F(x)=x+4$ and $g (x) = x^{2}$ $g(x)=x^2$ ?

1 Answer

Explanation:

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How do you find the compositions given F(x)=x+4F(x)=x+4F(x)=x+4 and g(x)=x^2g(x)=x2g(x)=x^2?

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Explanation:

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How do you find the compositions given $F (x) = x + 4$ $F(x)=x+4$ and $g (x) = x^{2}$ $g(x)=x^2$ ?