5-5 Part 2: Function Operations

Perform the indicated operation.

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• 
• 
• 

Answer explanation

• 3x² - 9

• 12x² + 8x + 5

• 16x² - 36x + 20

• 9x² + 18x + 5

• none of these

Answer explanation

 $\left(f\circ h\right)\left(x\right)=f\left(3x+3\right)$  
 $=\left(3x+3\right)^2-4$  
 $=\left(3x+3\right)\left(3x+3\right)-4$  
 $=\left(9x^2+9x+9x+9\right)-4$  
 $=9x^2+18x+5$  

p(x) = 3x + 4

q(x) = 2x²

Find q(p(-2))

• 8

• -8

• 28

• None of these.

Answer explanation

First find p(-2) = 3(-2) + 4
p(-2) = -2

Now substitute that value into q(x)
$q\left(-2\right)=2\left(-2\right)^2$
$=2\left(4\right)$
$=8$

Given f(x) = 3x + 10
and g(x) = x - 2
Find f(g(5))

• 19
• 23
• -10
• None of these.

Given f(x)= -3x + 7 and g(x)=2x² - 8, find g(f(x)).

• g(f(x))= -6x² + 31
• g(f(x))= -6x² + 24
• g(f(x))=18x² - 84x + 90
• g(f(x))=9x² - 42x - 41

Which expression represents g(f(x)) if 
f(x) = 2x - 8 and
g(x) = 4x

• 8x - 32
• 8x² - 32x
• 8x - 8
• 6x - 8

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of f(g(4)).

• 182
• 40
• 61
• None of the Above