Understanding Engineering Mathematics

(iii) f(x)= 2 x^2 −x+1(iv)f(x)=

1

x+ 2

x=− 2

(v) f(x)=

3 x− 1

2 x+ 1

x=−

1

2

B.Iff(x)=

x^2 − 1

x+ 2

obtain expressions for

(i) f(u) (ii) f(t+ 1 ) (iii) f

(s

t

)

(iv) f(a+h) (v) f(x+δx)

3.3.2 Plotting the graph of a function

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A.Plot the graphs of the following functions over the ranges indicated:

(i) 2x^3 − 3 ≤x≤ 3 (ii)

3

x

− 6 ≤x≤ 6 (iii) 2x − 4 ≤x≤ 4

B.Plot the graph of the functionf(x)= 2 x^2 − 3 x−2 and confirm the statement made

in Section 3.3.6 about the range of values ofxfor which this function is positive.

3.3.3 Formulae

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The following are examples of standard formulae occurring in engineering, with standard

notation. In each case define the variables, explain what the formula tells us, and describe

the type of function that the left-hand side is of the bracketed variables. Make the indicated

variable the subject of the formula.

(i) V=IR (R) (ii) P=I^2 R(R)

(iii) E=^12 mv^2 (v)(iv)s=ut+^12 at^2 (t)

(v) E=mc^2 (c)

3.3.4 Odd and even functions

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State whether the following functions are even, odd or neither.

(i) 2x (ii) 3x^2 − 1

(iii) 2x^3 −x (iv) x^2 + 2 x+ 1

(v) cosx (vi) x^4 + 2 x^2 + 1

(vii) sinx (viii) ex

3.3.5 Composition of functions

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Ifg(x)=x^2 +1,f(x)=

x

x− 1

determine the compositionsf(g(x))andg(f(x)).