Weekly Test - 01 ( Opt. Math )

If f(x) & g(x) are two polynomials, under which of the following condition, f(x)÷g(x) is undefined ?

• for f(x) = 0

• for g(x) = 0

• Both B & C

• None of the above

• 1

• 2

• 3

• 4

According to Cramer's rule, In a simultaneous equation, if D = 2, D_x = 8 and D_y = 6. What is the value of y in the simultaneous equation ?

• 1

• 2

• 3

• 4

• 30°

• 60°

• 90°

• None of the above

For any two equal angles A & B, what will be the value of cos(A+B)?

• sin(A/2)

• cos(A/2)

• sin2A

• cos2A

i) Define composite function. [ 1 ]

ii) If functions f = {(1, x), (2, y), (3, z)}

and g = {(a, 1), (b, 2), (c, 3)}, show the composite functions fog and gof in arrow diagram. [ 1 + 1 ]

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Define inverse function. If g(x)=−10x+6 find the value of g^-1(2). [ 1 + 1 ]

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i) For what value of x will the function f(x) = 2x-3 becomes an identity function. [ 1 ]

ii) If g(x) = ( x-2 )/3 and h(x) = 3x+2, prove that gh(x) is an identity function. [ 1 + 1 ]

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If f(x)=4x+5 and fog(x)=8x+13 then find g(x) and gof(x). [ 1 + 1 ]

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If f(x) = 2x+7, evaluate : *[ 1 marks each ]

i) ff(4)

ii) f(x+2)

iii) f^-1(x+2).

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