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24 Cards in this Set
- Front
- Back
Give the definition of an inverse function g(x) of a function f(x)
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Let f(x) have a domain D and range R. If there is a function g(x) with domain R such that g(f(x))=x for xED and f(g(x))= x for ER then f(x) is said to be invertible. the function g(x) is calle the inverse function and is denoted f^-1(x). THe inverse of f(x) denoted (f^-1(x), is the function that reverses the effect of f(x)
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Des every function have an inverse function
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No. f(x)=x^2 does not have an inverse because it is not one to one
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what is marginal cost and why is it reasonable to use a derivative to estimate it
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marginal cost is the cost of producing another unit. = (x+1) - c(x). the derivative is the instantaneous rate of change, marginal cos tis the difference in cost of adding and additional unit
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(fg)'
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f'g+fg'
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(cf)'
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cf'
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(f/g)'
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gf'-fg'/g^2
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inverse fo f(x)
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g'(x)=1/f'(g(x))
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(f(g(x))'
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f'(g(x))*g'(x)
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(sinx)'
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cosx
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(cosx)'
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-sinx
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(tanx)'
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sec^2x
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(secx)'
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secxtanx
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(csc)'
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-cosxcotx
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(cotx)'
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-cos^2x
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(sin^-1(x))'
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1/sqrt(1-x^2)
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(cos^-1(x))'
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-1/sqrt(1-x^2)
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(tan^-1(x))'
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1/1+x^2
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(cot^-1(x))'
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-1/1+x^2
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(sec^-1(x))'
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1/abs(x)sprt(x^2-1)
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(csc^-1(x))'
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-1/abs(x)sprt(x^2-1)
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(e^x)'
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e^x
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(ln(x))'
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1/x
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(b^x)'
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ln(b)*b^x
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(logbx)'
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1/ln(b)*(x)'/x
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