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Study Guides > MATH 1314: College Algebra

Key Concepts & Glossary

Key Concepts

  • If g(x)g\left(x\right) is the inverse of f(x)f\left(x\right), then
  • g(f(x))=f(g(x))=xg\left(f\left(x\right)\right)=f\left(g\left(x\right)\right)=x.
  • Each of the toolkit functions has an inverse.
  • For a function to have an inverse, it must be one-to-one (pass the horizontal line test).
  • A function that is not one-to-one over its entire domain may be one-to-one on part of its domain.
  • For a tabular function, exchange the input and output rows to obtain the inverse.
  • The inverse of a function can be determined at specific points on its graph.
  • To find the inverse of a formula, solve the equation y=f(x)y=f\left(x\right) for xx as a function of yy. Then exchange the labels xx and yy.
  • The graph of an inverse function is the reflection of the graph of the original function across the line y=xy=x.

Glossary

inverse function
for any one-to-one function f(x)f\left(x\right), the inverse is a function f1(x){f}^{-1}\left(x\right) such that f1(f(x))=x{f}^{-1}\left(f\left(x\right)\right)=x for all xx in the domain of ff; this also implies that f(f1(x))=xf\left({f}^{-1}\left(x\right)\right)=x for all xx in the domain of f1{f}^{-1}

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