Operations and Composition of Functions

Authored by Brayden Teele

Mathematics

9th - 12th Grade

CCSS covered

Used 96+ times

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15 questions

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FILL IN THE BLANKS QUESTION

10 mins • 1 pt

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$h\left(9\right)+f\left(2\right)$

(a)

Tags

CCSS.HSF.IF.A.2

FILL IN THE BLANKS QUESTION

10 mins • 1 pt

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$k\left(-7\right)-g\left(8\right)$

(a)

Tags

CCSS.HSF.IF.A.2

FILL IN THE BLANKS QUESTION

10 mins • 1 pt

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$\left(k\ \circ\ g\right)\left(2\right)$

(a)

Tags

CCSS.HSF-BF.A.1C

FILL IN THE BLANKS QUESTION

10 mins • 1 pt

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$f\left(g\left(h\left(3\right)\right)\right)$

(a)

Tags

CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$\left(k-g\right)\left(x\right)$

$-x^2-3x-4$

$-x^2-3x+4$

$3x^2-3x-4$

$x^2-3x+4$

Tags

CCSS.HSF-BF.A.1B

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$\left(k\ \circ\ f\right)\left(x\right)$

$36x^2-42x+10$

$6x^2-18x-2$

$4x^2-24x$

Tags

CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$\left(k\ \circ\ f\right)\left(2\right)$

$70$

$-14$

$-20$

$8$

Tags

CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$\left(k-f\right)\left(x\right)$

$x^2-9x+2$

$x^2-9x-2$

$-x^2+9x-2$

$-x^2-9x+2$

Tags

CCSS.HSF-BF.A.1B

FILL IN THE BLANKS QUESTION

10 mins • 1 pt

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$f\left(h\left(g\left(k\left(1\right)\right)\right)\right)$

(a)

Tags

CCSS.HSF-BF.A.1C

10.

FILL IN THE BLANKS QUESTION

10 mins • 1 pt

Click on the functions above to see easier.
Evaluate $\left(g\ \circ\ f\right)\left(7\right)$

(a)

Tags

CCSS.HSF-BF.A.1C

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Operations and Composition of Functions

Given that f(x)=6x−2f\left(x\right)=6x-2f(x)=6x−2 , g(x)=2x2+4g\left(x\right)=2x^2+4g(x)=2x2+4 , h(x)=3−2xh\left(x\right)=3-2xh(x)=3−2x and k(x)=x2−3xk\left(x\right)=x^2-3xk(x)=x2−3x , evaluate the following h(9)+f(2)h\left(9\right)+f\left(2\right)h(9)+f(2) (a)

Given that f(x)=6x−2f\left(x\right)=6x-2f(x)=6x−2 , g(x)=2x2+4g\left(x\right)=2x^2+4g(x)=2x2+4 , h(x)=3−2xh\left(x\right)=3-2xh(x)=3−2x and k(x)=x2−3xk\left(x\right)=x^2-3xk(x)=x2−3x , evaluate the following k(−7)−g(8)k\left(-7\right)-g\left(8\right)k(−7)−g(8) (a)

Given that f(x)=6x−2f\left(x\right)=6x-2f(x)=6x−2 , g(x)=2x2+4g\left(x\right)=2x^2+4g(x)=2x2+4 , h(x)=3−2xh\left(x\right)=3-2xh(x)=3−2x and k(x)=x2−3xk\left(x\right)=x^2-3xk(x)=x2−3x , evaluate the following (k ∘ g)(2)\left(k\ \circ\ g\right)\left(2\right)(k ∘ g)(2) (a)

Given that f(x)=6x−2f\left(x\right)=6x-2f(x)=6x−2 , g(x)=2x2+4g\left(x\right)=2x^2+4g(x)=2x2+4 , h(x)=3−2xh\left(x\right)=3-2xh(x)=3−2x and k(x)=x2−3xk\left(x\right)=x^2-3xk(x)=x2−3x , evaluate the following f(g(h(3)))f\left(g\left(h\left(3\right)\right)\right)f(g(h(3))) (a)

Given that f(x)=6x−2f\left(x\right)=6x-2f(x)=6x−2 , g(x)=2x2+4g\left(x\right)=2x^2+4g(x)=2x2+4 , h(x)=3−2xh\left(x\right)=3-2xh(x)=3−2x and k(x)=x2−3xk\left(x\right)=x^2-3xk(x)=x2−3x , evaluate the following (k−g)(x)\left(k-g\right)\left(x\right)(k−g)(x)

Given that f(x)=6x−2f\left(x\right)=6x-2f(x)=6x−2 , g(x)=2x2+4g\left(x\right)=2x^2+4g(x)=2x2+4 , h(x)=3−2xh\left(x\right)=3-2xh(x)=3−2x and k(x)=x2−3xk\left(x\right)=x^2-3xk(x)=x2−3x , evaluate the following (k ∘ f)(x)\left(k\ \circ\ f\right)\left(x\right)(k ∘ f)(x)

Given that f(x)=6x−2f\left(x\right)=6x-2f(x)=6x−2 , g(x)=2x2+4g\left(x\right)=2x^2+4g(x)=2x2+4 , h(x)=3−2xh\left(x\right)=3-2xh(x)=3−2x and k(x)=x2−3xk\left(x\right)=x^2-3xk(x)=x2−3x , evaluate the following (k ∘ f)(2)\left(k\ \circ\ f\right)\left(2\right)(k ∘ f)(2)

Given that f(x)=6x−2f\left(x\right)=6x-2f(x)=6x−2 , g(x)=2x2+4g\left(x\right)=2x^2+4g(x)=2x2+4 , h(x)=3−2xh\left(x\right)=3-2xh(x)=3−2x and k(x)=x2−3xk\left(x\right)=x^2-3xk(x)=x2−3x , evaluate the following (k−f)(x)\left(k-f\right)\left(x\right)(k−f)(x)

Click on the functions above to see easier.Evaluate (g ∘ f)(7)\left(g\ \circ\ f\right)\left(7\right)(g ∘ f)(7) (a)

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Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$h\left(9\right)+f\left(2\right)$

(a)

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$k\left(-7\right)-g\left(8\right)$

(a)

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$\left(k\ \circ\ g\right)\left(2\right)$

(a)

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$f\left(g\left(h\left(3\right)\right)\right)$

(a)

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$\left(k-g\right)\left(x\right)$

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$\left(k\ \circ\ f\right)\left(x\right)$

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$\left(k\ \circ\ f\right)\left(2\right)$

Given that
$f\left(x\right)=6x-2$ , $g\left(x\right)=2x^2+4$ , $h\left(x\right)=3-2x$ and $k\left(x\right)=x^2-3x$ , evaluate the following

$\left(k-f\right)\left(x\right)$

Click on the functions above to see easier.
Evaluate $\left(g\ \circ\ f\right)\left(7\right)$

(a)