Computational Mathmatics

Victorian Institute of Technology Pty Ltd

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ITSU2011 – Computational Mathematics Page 1 of 4

ITSU2011

Computational Mathematics

Activity 07

Victorian Institute of Technology Pty Ltd

ABN: 41 085 128 525 RTO No: 20829 TEQSA ID: PRV14007 CRICOS Provider Code: 02044E

ITSU2011 – Computational Mathematics Page 2 of 4

Part A)

1) Let 𝑓(𝑥) = 𝑥 2 − 𝑥 + 5, 𝑥 ≤ 2.

A) Sketch, state the domain and range 𝑓(𝑥).

B) Find the inverse function of 𝑓(𝑥).

C) Find the domain and range of 𝑓 −1(𝑥).

2) Below is shown the graph of 𝑓(𝑥) = √2𝑥 − 3

A) Sketch the inverse of 𝑓(𝑥) in the same graph.

B) Find the inverse of 𝑓(𝑥) and state the domain and range.

2)

A) What is the domain of 𝑓 −1(𝑥).

Victorian Institute of Technology Pty Ltd

ABN: 41 085 128 525 RTO No: 20829 TEQSA ID: PRV14007 CRICOS Provider Code: 02044E

ITSU2011 – Computational Mathematics Page 3 of 4

B) Sketch the inverse.

C) Find 𝑓 −1(𝑥), state the domain and range.

4) Below are shown the graph of 6 functions. Sketch the graph of the inverse of each function.

Victorian Institute of Technology Pty Ltd

ABN: 41 085 128 525 RTO No: 20829 TEQSA ID: PRV14007 CRICOS Provider Code: 02044E

ITSU2011 – Computational Mathematics Page 4 of 4

Part B)

1) Calculate (f ∘ g) (x) using f(x) = 2x + 3 and g(x) = -x 2 + 1.

2) If f(x) = 3x − 1 and g(x) = x2, then what is (f ° g)(x)?

3) If f(x) = 2x and g(x) = 2x, then what is (g ° f)(x)?

4) f and g are both defined on the set of real numbers

f(x) = x2

g(x) = x + 2

For what value of x does (f ° g)(x) = (g ° f)(x)?

5) f and g are both defined on the set of real numbers and c is a constant

f(x) = cx − 3

g(x) = cx + 5

If (f ° g)(x) = (g ° f)(x) for all values of x, what is the value of c?