1) f(x)=-3x+2 g(x)=3x^2-x+2 find (f+g)(x) 2) f(x)=x-1  g(x)=2x^2-2x-5 find g(f(x)) 3) f(x)=3x+2  g(x)=-2x^2-3x+5  find g(f(x)) 4) f(x)=2x+3  g(x)=2x^2+2x  find f(g(x))

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baxthum8 | High School Teacher | (Level 3) Associate Educator

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#1)  `f(x) = -3x + 2`

` g(x) = 3x^2-x + 2`

`(f+g)x = -3x + 2 + 3x^2 - x + 2` 

Therefore,`<br>`

`(f+g)x = 3x^2 - 4x + 4`

` `#2)  `f(x) = x - 1`

 `g(x) = 2x^2 - 2x - 5`

`g(f(x)) = 2(x-1)^2 - 2(x-1) - 5`

`g(f(x)) = 2(x^2-2x+1) -2(x-1)-5`

`g(f(x)) = 2x^2 - 4x + 2 - 2x + 2 - 5`

Therefore,  

`g(f(x)) = 2x^2 - 6x - 1`   

#3)  `f(x) = 3x + 2`

`g(x) = 2x^2 - 3x +5`

` `Find g(f(x)).

`g(f(x)) = 2(3x+2)^2 - 3(3x + 2) + 5`

` ` `g(f(x)) = 2(9x^2 + 12x + 4) - 3(3x+2) + 5`

`g(f(x)) = 18x^2 + 24x + 8 - 9x - 6 + 5`  

Therefore, 

`g(f(x)) = 18x^2 + 15x + 7`

#4)  `f(x) = 2x + 3`

`g(x) = 2x^2 + 2x`

Find f(g(x)).

`f(g(x)) = 2(2x^2 + 2x) + 3`

Therefore,

`f(g(x)) = 4x^2 + 4x + 3`

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