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Grade 12

Composite Functions

Interactive practice questions

Given the functions $f\left(x\right)=4x-10$f(x)=4x10 and $g\left(x\right)=3+\frac{4}{x}$g(x)=3+4x, evaluate $f\left(g\left(2\right)\right)$f(g(2)).

Easy
2min

Consider the functions $f\left(x\right)=-2x-3$f(x)=2x3 and $g\left(x\right)=-2x-6$g(x)=2x6.

Easy
3min

Consider the functions $f\left(x\right)=-2x-8$f(x)=2x8 and $g\left(x\right)=4x^2-4$g(x)=4x24.

Easy
5min

Consider the functions $f\left(x\right)=-2x+2$f(x)=2x+2, $g\left(x\right)=4x^2-8$g(x)=4x28 and $r\left(x\right)=-3x-8$r(x)=3x8.

Easy
2min
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Outcomes

12F.D.2.4

Determine the composition of two functions [i.e., f(g(x))] numerically (i.e., by using a table of values) and graphically, with technology, for functions represented in a variety of ways, and interpret the composition of two functions in real-world applications

12F.D.2.5

Determine algebraically the composition of two functions [i.e., f(g(x))], verify that f(g(x)) is not always equal to g( f(x)) and state the domain and the range of the composition of two functions

12F.D.2.6

Solve problems involving the composition of two functions, including problems arising from real-world applications

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