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  1. Problems
  2. /Functions and Calculus
  3. /Composite and Inverse Functions

Composite and Inverse Functions

Mathematics
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More in Functions and CalculusSets and IntervalsRelations and FunctionsGraphs of FunctionsComposite and Inverse FunctionsFunctions as Models of DataFunctional EquationsCounting Functions
10 problems
Type:
1.
Let f(x) = x - 4 and g(x) = 2x. Find (g ° f)⁻¹, and check that it equals f⁻¹ ° g⁻¹ but not g⁻¹ °…
High School (11–12) · Composite and Inverse FunctionsStemPy LabStemPy Lab
Medium
2.
A has 3 elements and B has 6 elements. How many functions are there from A to B?
High School (11–12) · Composite and Inverse FunctionsStemPy LabStemPy Lab
Medium
3.
f(x) = -x² + 9 is a function from ℝ to ℝ. Is it onto? Change the codomain so that it becomes onto.
High School (11–12) · Composite and Inverse FunctionsStemPy LabStemPy Lab
Easy
4.
Show that f(x) = 4 - 3x is one-one. Show that g(x) = x² + 6x is not one-one on ℝ.
High School (11–12) · Composite and Inverse FunctionsStemPy LabStemPy Lab
Medium
5.
Find the inverse of f(x) = (2x + 5)/(x - 3). Give the domain and the range of f.
High School (11–12) · Composite and Inverse FunctionsStemPy LabStemPy Lab
Medium
6.
Write h(x) = 1/((3x - 1)²) as a composite of three simple functions.
High School (11–12) · Composite and Inverse FunctionsStemPy LabStemPy Lab
Easy
7.
Let f(x) = 2x + 3 and g(x) = ax + b. For which a and b is g ° f = f ° g?
High School (11–12) · Composite and Inverse FunctionsStemPy LabStemPy Lab
Hard
8.
Let f(x) = 1/(x + 2) and g(x) = √x. Find (g ° f)(x) and (f ° g)(x), with their domains.
High School (11–12) · Composite and Inverse FunctionsStemPy LabStemPy Lab
Hard
9.
Let f(x) = √(x + 5) and g(x) = x² - 4. Find the domain of f + g and the domain of f/g.
High School (11–12) · Composite and Inverse FunctionsStemPy LabStemPy Lab
Medium
10.
Let f(x) = x + 5 and g(x) = 4x - 1. Find (g ° f)(x) and (f ° g)(x), and their values at x = 3.
High School (11–12) · Composite and Inverse FunctionsStemPy LabStemPy Lab
Easy