Given f ( x ) = 4 x − 4 f\left(x\right)=\sqrt{4x-4} f ( x ) = 4 x − 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> and g ( x ) = 3 x + 1 g\left(x\right)=3x+1 g ( x ) = 3 x + 1 , find ( f ∘ g ) ( 3 ) \left(f\circ g\right)\left(3\right) ( f ∘ g ) ( 3 ) in simplest form.

2 2 2\sqrt{2} 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

34 \sqrt{34} 3 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Composite Functions

Authored by Yan Liu

Mathematics

11th Grade

CCSS covered

Used 22+ times

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Given $f\left(x\right)=5x+7$ and $g\left(x\right)=3+4x$ , find $\left(f\circ g\right)\left(x\right)$ in simplest form.

$15+16x$

$31+20x$

$22+20x$

$42+25x$

Tags

CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Given $f\left(x\right)=5x+7$ and $g\left(x\right)=3+4x$ , find $\left(g\circ g\right)\left(x\right)$ in simplest form.

$15+16x$

$31+20x$

$22+20x$

$42+25x$

Tags

CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Given $f\left(x\right)=5x+7$ and $g\left(x\right)=3+4x$ , find $\left(g\circ f\right)\left(x\right)$ in simplest form.

$15+16x$

$31+20x$

$22+20x$

$42+25x$

Tags

CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Given $f\left(x\right)=5x+7$ and $g\left(x\right)=3+4x$ , find $\left(f\circ f\right)\left(x\right)$ in simplest form.

$42+25x$

$31+20x$

$22+20x$

$15+16x$

Tags

CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Given $f\left(x\right)=5x+7$ and $g\left(x\right)=3+4x$ , find $\left(f\circ f\right)\left(1\right)$ in simplest form.

$31$

$51$

$42$

$67$

Tags

CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Given $f\left(x\right)=3x-6$ and $g\left(x\right)=x^2+4$ , find $\left(f\circ g\right)\left(x\right)$ in simplest form.

$3x^2+12$

$3x^2-6$

$3x^2+6$

$3x^2-12$

Tags

CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Given $f\left(x\right)=3x-6$ and $g\left(x\right)=x^2+4$ , find $\left(g\circ f\right)\left(x\right)$ in simplest form.

$9x^2-36x$

$9x^2+42$

$9x^2+36x-42$

$9x^2-36+40$

Tags

CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Given $f\left(x\right)=3x-6$ and $g\left(x\right)=x^2+4$ , find $\left(g\circ f\right)\left(-1\right)$

Tags

CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Given $f\left(x\right)=3x-6$ and $g\left(x\right)=x^2+4$ , find $\left(f\circ f\right)\left(2\right)$

-8

-6

Tags

CCSS.HSF-BF.A.1C

10.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Given $f\left(x\right)=\sqrt{4x-4}$ and $g\left(x\right)=3x+1$ , find $\left(g\circ g\right)\left(x\right)$ in simplest form.

$9x+4$

$12x-2$

$12x-6$

$9x+3$

Tags

CCSS.HSF-BF.A.1C

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Composite Functions

Given f(x)=5x+7f\left(x\right)=5x+7f(x)=5x+7 and g(x)=3+4xg\left(x\right)=3+4xg(x)=3+4x , find (f∘g)(x)\left(f\circ g\right)\left(x\right)(f∘g)(x) in simplest form.

Given f(x)=5x+7f\left(x\right)=5x+7f(x)=5x+7 and g(x)=3+4xg\left(x\right)=3+4xg(x)=3+4x , find (g∘g)(x)\left(g\circ g\right)\left(x\right)(g∘g)(x) in simplest form.

Given f(x)=5x+7f\left(x\right)=5x+7f(x)=5x+7 and g(x)=3+4xg\left(x\right)=3+4xg(x)=3+4x , find (g∘f)(x)\left(g\circ f\right)\left(x\right)(g∘f)(x) in simplest form.

Given f(x)=5x+7f\left(x\right)=5x+7f(x)=5x+7 and g(x)=3+4xg\left(x\right)=3+4xg(x)=3+4x , find (f∘f)(x)\left(f\circ f\right)\left(x\right)(f∘f)(x) in simplest form.

Given f(x)=5x+7f\left(x\right)=5x+7f(x)=5x+7 and g(x)=3+4xg\left(x\right)=3+4xg(x)=3+4x , find (f∘f)(1)\left(f\circ f\right)\left(1\right)(f∘f)(1) in simplest form.

Given f(x)=3x−6f\left(x\right)=3x-6f(x)=3x−6 and g(x)=x2+4g\left(x\right)=x^2+4g(x)=x2+4 , find (f∘g)(x)\left(f\circ g\right)\left(x\right)(f∘g)(x) in simplest form.

Given f(x)=3x−6f\left(x\right)=3x-6f(x)=3x−6 and g(x)=x2+4g\left(x\right)=x^2+4g(x)=x2+4 , find (g∘f)(x)\left(g\circ f\right)\left(x\right)(g∘f)(x) in simplest form.

Given f(x)=3x−6f\left(x\right)=3x-6f(x)=3x−6 and g(x)=x2+4g\left(x\right)=x^2+4g(x)=x2+4 , find (g∘f)(−1)\left(g\circ f\right)\left(-1\right)(g∘f)(−1)

Given f(x)=3x−6f\left(x\right)=3x-6f(x)=3x−6 and g(x)=x2+4g\left(x\right)=x^2+4g(x)=x2+4 , find (f∘f)(2)\left(f\circ f\right)\left(2\right)(f∘f)(2)

Given f(x)=4x−4f\left(x\right)=\sqrt{4x-4}f(x)=4x−4​ and g(x)=3x+1g\left(x\right)=3x+1g(x)=3x+1 , find (g∘g)(x)\left(g\circ g\right)\left(x\right)(g∘g)(x) in simplest form.

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Given $f\left(x\right)=5x+7$ and $g\left(x\right)=3+4x$ , find $\left(f\circ g\right)\left(x\right)$ in simplest form.

Given $f\left(x\right)=5x+7$ and $g\left(x\right)=3+4x$ , find $\left(g\circ g\right)\left(x\right)$ in simplest form.

Given $f\left(x\right)=5x+7$ and $g\left(x\right)=3+4x$ , find $\left(g\circ f\right)\left(x\right)$ in simplest form.

Given $f\left(x\right)=5x+7$ and $g\left(x\right)=3+4x$ , find $\left(f\circ f\right)\left(x\right)$ in simplest form.

Given $f\left(x\right)=5x+7$ and $g\left(x\right)=3+4x$ , find $\left(f\circ f\right)\left(1\right)$ in simplest form.

Given $f\left(x\right)=3x-6$ and $g\left(x\right)=x^2+4$ , find $\left(f\circ g\right)\left(x\right)$ in simplest form.

Given $f\left(x\right)=3x-6$ and $g\left(x\right)=x^2+4$ , find $\left(g\circ f\right)\left(x\right)$ in simplest form.

Given $f\left(x\right)=3x-6$ and $g\left(x\right)=x^2+4$ , find $\left(g\circ f\right)\left(-1\right)$

Given $f\left(x\right)=3x-6$ and $g\left(x\right)=x^2+4$ , find $\left(f\circ f\right)\left(2\right)$

Given $f\left(x\right)=\sqrt{4x-4}$ and $g\left(x\right)=3x+1$ , find $\left(g\circ g\right)\left(x\right)$ in simplest form.