if p(x)= 2x² - 4x and q(x) = x - 3, what is the value of q(p(5))/p(q(5))?

Solution:

Given, p(x) = 2x² - 4x

q(x) = x - 3 

We have to find the value of q(p(5))/p(q(5))

q(p(x)) = q(2x² - 4x)

= 2x² - 4x - 3

Put x = 5 in the above expression,

q(p(5)) = 2(5)² - 4(5) - 3

= 2(25) - 20 - 3

= 50 - 23

= 27

p(q(x)) = p(x - 3)

= 2(x - 3)² - 4(x - 3)

= 2(x² - 6x + 9) - 4x + 12

= 2x² - 12x + 18 - 4x + 12

= 2x² - 16x + 30

Put x = 5 in the above expression,

p(q(5)) = 2x² - 16x + 30

= 2(5)² - 16(5) + 30

= 2(25) - 80 + 30

= 50 - 50

= 0

So, q(p(5))/p(q(5)) = 27/0 = Not defined

Therefore, the value of q(p(5))/p(q(5)) is Not defined.

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if p(x)= 2x² - 4x and q(x) = x - 3, what is the value of q(p(5))/p(q(5))?

Summary:

If p(x)= 2x² - 4x and q(x)= x - 3, the value of q(p(5))/p(q(5)) is Not defined.