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VCE 12 Methods 2023

2.05 Inverse functions

Interactive practice questions

Consider the function given by $f\left(x\right)=x+5$f(x)=x+5.

a

Sketch the graph of $f\left(x\right)$f(x) on the coordinate plane below:

Loading Graph...
b

Is the function $f\left(x\right)$f(x) one-to-one?

No

A

Yes

B
c

Does an inverse function exist for $f\left(x\right)$f(x)?

No

A

Yes

B
Easy
< 1min

Consider the function given by $f\left(x\right)=\frac{2x+3}{2}$f(x)=2x+32.

Easy
1min

Consider the function given by $f\left(x\right)=\left(x-2\right)\left(x+3\right)$f(x)=(x2)(x+3).

Easy
1min

Consider the function given by $f\left(x\right)=x^2-1$f(x)=x21.

Easy
1min
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Outcomes

U34.AoS1.3

transformation from y=f(x) to y=A(f(n(x+b))+c and f is one of the functions specified above, and the inverse transformation

U34.AoS1.4

the relation between the graph of an original function and the graph of a corresponding transformed function (including families of transformed functions for a single transformation parameter)

U34.AoS1.11

the concept of an inverse function, connection between domain and range of the original function and its inverse relation and the conditions for existence of an inverse function, including the form of the graph of the inverse function for specified functions

U34.AoS1.16

find the rule of an inverse function and give its domain and range

U34.AoS2.2

functions and their inverses, including conditions for the existence of an inverse function, and use of inverse functions to solve equations involving exponential, logarithmic, circular and power functions

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