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SLS - Math 11 - Ch 5.1-5.3 - Function Notation

Quiz yourself by thinking what should be in each of the black spaces below before clicking on it to display the answer.
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f(x)=2x-3, g(x)=x^2
Answer
f(3)+2g(-1)   5  
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(f+g)(x)   = x^2 + 2x - 3  
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(f-g)(x)   -x^2 + 2x - 3  
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(fg)(x)   2x^3 -3x^2  
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(f/g)(x)   = (2x - 3)/(x^2) restriction: x doesn't equal 0  
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When do you have to list restrictions?   Whenever there's an x on the bottom of a fraction. Sometimes teachers will NOT take off marks. But you're safest to write it each time.  
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f(g(x))   2x^2 - 3  
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f(f(x))   4x - 9  
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g(g(x))   x^4  
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(fg)(-3)   -81  
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f(f(0))   -9  
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(g/f)(4)   16/5  
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the inverse of f(x)   (x + 3) / 2  
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the inverse of g(x)   square root of x  
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What are the steps to prove whether or not f(x) and g(x) are inverses of eachother?   Plug each function into the x variable of the other. If both simplify to x, they are inverses.  
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Created by: slscarrie
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