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6 Cards in this Set
- Front
- Back
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Given the recursive formula, write the explicit formula for the sequence.
t₁=0 t[n]=t[n-1]-3 NOTE: quantities in brackets are subscripts. |
t[n]=t₁+d(n-1)
t[n]=t₁+3(n-1) NOTE: quantities in brackets are subscripts |
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Write an explicit and recursive formula for the sequence: 3, 9, 27, 81....
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Explicit a[n]=3ⁿ
Recursive a₁=3 a[n]=3a[n]-1 NOTE: quantities in brackets are subscripts |
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Given t(x)=7x-2 and v(x)=x²+2, evaluate the composition of v(t(4)).
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t(4)=7x-2
t(4)=7(4)-2 t(4)=28-2 t(4)=26 v(x)=x²+2 v(26)=26²+2 v(26)=676+2 v(26=678 v(t(4))=678 |
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Let f be the function that assigns to a temperature in degrees Celcius its equivalent in degrees Fahrenheit. Let g be the function that assigns to a temperature in degrees Kelvin its equivalent in degrees Celsius. What do x and f(g(x)) represent in terms of temperatures?
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Given a temperature x in degrees Kelvin, g(x) represents its equivalent in degrees Celsius. Given a temperature g(x) in degrees Celsius, f(g(x)) represents its equivalent in degrees Fahreheit. Combining these two statements, if x represents a temperature in degrees Kelvin, then f(g(x)) represents its equivalent in degrees Fahrenheit.
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Let f be the function that assigns to a temperature in degrees Celcius its equivalent in degrees Fahrenheit. Let g be the function that assigns to a temperature in degrees Kelvin its equivalent in degrees Celsius. Given that f(x)=9/5x+32 and g(x)=x-273, find an expression for f(g(x)).
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f(g(x))= 9/5(g(x))+32
f(g(x))=9/5(x-273)+32 f(g(x))=9/5x-2297/5 |
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Let f be the function that assigns to a temperature in degrees Celcius its equivalent in degrees Fahrenheit. Let g be the function that assigns to a temperature in degrees Kelvin its equivalent in degrees Celsius. Find an expression for the function h which assigns to a temperature in degrees Fahrenheit its equivalent in degrees Kelvin.
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In order to find function h, we must reverse the process used to find f(g(x)).
h(x)=5/9(x+2297/5) h(x)=5/9x+2297/9 |
