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Mathematics > Course Model Precalculus (Advanced Course) > Building Functions
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Mathematics | Course : Model Precalculus (Advanced Course)

Domain - Building Functions

Cluster - Build new functions from existing functions.

[PC.F-BF.B.4.b] - (+) Verify by composition that one function is the inverse of another.

Resources:


  • Function
    A mathematical relation for which each element of the domain corresponds to exactly one element of the range.
  • Inverse function
    A function obtained by expressing the dependent variable of one function as the independent variable of another; that is the inverse of y = f(x) is x = f –1(y).
  • Financial Applications Of Inverse Functions

Predecessor Standards:

No Predecessor Standards found.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • AI.F-IF.A.1
    Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output (range) of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
  • AI.F-BF.B.4.a
    Solve an equation of the form f(x) = c for a linear function f that has an inverse and write an expression for the inverse.
  • MI.F-IF.A.1
    Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
  • MII.F-BF.B.4.a
    Solve an equation of the form f(x) = c for a linear function f that has an inverse and write an expression for the inverse.
  • MIII.F-BF.B.4.a
    Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x3 or f(x) = (x + 1)/(x - 1) for x ≠ 1.
  • MIII.F-LE.A.4
    For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.*
  • PC.F-BF.B.5
    (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
  • PC.F-TF.B.6
    (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
  • PC.F-TF.B.7
    (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.*
  • AQR.F-TF.B.7
    (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.*