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Type: Multiple-Choice
Category: Functions and Relations
Level: Grade 11
Standards: HSF-BF.A.1, HSF-BF.A.1b
Author: nsharp1
Created: 5 years ago

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Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b

$f(x) = {{:(6 , 0 <= x <4),(-x+10, 4 <= x <7),(3, 7 <= x <=10):}$ and

$g(x) = 1/(x-1)$ , find

$(f+g)(x)$ and its domain.

$(f+g)(x) = {{:( (6x \ - \ 5)/(x \ - \ 1) , 0 <=x<4"," \ x!=1), ((-x^2 \ + \ 11x \ - \ 9)/(x \ - \ 1), 4 <= x <7),((3x \ - \ 2)/(x \ - \ 1), 7 <= x <=10):}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$
$(f+g)(x) = {{:( (6)/(x \ - \ 1) , 0 <= x <4"," \ x!=1),((-x \ + \ 11)/(x \ - \ 1), 4 <= x <7),((4)/(x \ - \ 1), 7 <= x <=10):}$
$(f+g)(x) = (-x^2 + 20x - 18)/(x-1); \ \ 0 <= x <= 10 " and " x!=1$
$(f+g)(x) = (-x^2 + 20x - 18)/(x-1); \ \ x!=1$