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For the pair of functions, f(x) = x + 4 and g(x) = 4x - 3, find the following.a) (fog)(x)b) (fog)(2)c) (gof)(x)d) (gof)(2)a) (fog)(x) = 4x + 1 (Simplify your answer.)b) (fog)(2)= (Simplify your answer.)ingotscessessLibrary

User Sapph
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1 Answer

18 votes
18 votes

Question:

Solution:

Consider the following functions:


f(x)\text{ = x+4}
g(x)\text{ = }4x-3

then:


(f\circ g)(x)\text{ = f(g(x))= (4x-3)+4}

this is equivalent to:


(f\circ g)(x)\text{ =(4x-3)+4 = 4x +1}

thus:


(f\circ g)(x)\text{ =4x +1}

So, replacing x = 2 in the previous function we get:


(f\circ g)(2)\text{ =4(2) +1 = 9}

then:


(f\circ g)(2)\text{ = 9}

On the other hand, the composition:


(g\circ f)(x)\text{ = g(f(x)) = 4(x+4)-3}

this is equivalent to:


(g\circ f)(x)\text{ = 4(x+4)-3 = 4x +16-3 = 4x - 13}

then, we can conclude that:


(g\circ f)(x)\text{ =4x - 13}

So, replacing x = 2 in the previous function we get:


(g\circ f)(2)\text{ =4(2) - 13 = 8-13 = -5}

then:


(g\circ f)(2)\text{ =4(2) - 13 = 8-13 = -5}

then:


(g\circ f)(2)\text{ =-5}

Then the correct answers are:

1)


(f\circ g)(x)\text{ =4x +1}

2)


(f\circ g)(2)\text{ = 9}

3)


(g\circ f)(x)\text{ =4x - 13}

4)


(g\circ f)(2)\text{ =-5}
For the pair of functions, f(x) = x + 4 and g(x) = 4x - 3, find the following.a) (fog-example-1
User Janna Maas
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