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Algebra

Domain and range of a functionAlgebra

Identifying functionsAlgebra

Function notation (Advanced)Still Confused?

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Algebra

Domain and range of a functionAlgebra

Identifying functionsAlgebra

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An inverse function is a function that reverses all the operations of another function. Therefore, an inverse function has all the points of another function, except that the x and y values are reversed.

Basic concepts: Domain and range of a function, Identifying functions, Function notation (Advanced),

Related concepts: Derivative of inverse trigonometric functions, Derivative of logarithmic functions,

- 1.

• What is “inverse”, and what does “inverse” do to a function?

• Inverse: switch “x” and “y”

• Inverse: reflect the original function in the line “y = x” - 2.
**Graph an inverse**

Given the graph of $y = f\left( x \right)$ as shown,

a)Sketch the graph of the inverse $y = {f^{ - 1}}\left( x \right)$ in 2 ways:

i) by reflecting $f\left( x \right)$ in the line $y = x$

ii) by switching the x and y coordinates for each point on $f\left( x \right)$b)Is $f\left( x \right)$ a function?

Is ${f^{ - 1}}\left( x \right)$ a function? - 3.
**Inverse of a Quadratic Function**

Consider the quadratic function: $f(x) = (x+4)^2 + 2$a)Graph the function $f\left( x \right)$ and state the domain and range.b)Graph the inverse ${f^{ - 1}}\left( x \right)$ and state the domain and range.c)Is ${f^{ - 1}}\left( x \right)$ a function?

If not, describe how to restrict the domain of $f\left( x \right)$ so that the inverse of $f\left( x \right)$ can be a function. - 4.
**Determine the equation of the inverse.**

Algebraically determine the equation of the inverse ${f^{ - 1}}\left( x \right)$, given:a)$f\left( x \right) = - 5x + 4$b)$f\left( x \right) = {\left( {7x - 8} \right)^3} - 1$c)$f\left( x \right) = \frac{{3x}}{{2 + x}}$

20.

Functions

20.1

Function notation

20.2

Operations with functions

20.3

Adding functions

20.4

Subtracting functions

20.5

Multiplying functions

20.6

Dividing functions

20.7

Composite functions

20.8

Inequalities of combined functions

20.9

Inverse functions

20.10

One to one functions

20.11

Difference quotient: applications of functions

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