Question no. 7 Prove that is an odd function Solution: Question no. 8 Express the quadratic polynomial in complete square form. x2 + 4x + 6 Solution: x2 + 4x + 6 = x2 + 4x + 4 - 4 + 6 = (x+2)2 +2 Question no. 9 If the functions is defined by f then find the range of f. Solution: Since i.e., x 5 ,1/x 1/5.. f(x) 1/5. ≤ ≥ ≥ Question no. 10 If the functions and are defined by f g then Calculate gf(2). Solution: gf(x) = g(f(x)) = g(3/x) = 5(3/x) 1 = (15/x) 1. – – So, gf(2) = (15/2) 1 =13/2 – Question no. 11 If the functions is defined by g then find an expression in terms of for x .
Question no. 7 Prove that is an odd function Solution: Question no. 8 Express the quadratic polynomial x2 + 4x + 6 in complete square form. Solution: x2 + 4x + 6 = x2 + 4x + 4 - 4 + 6 = (x+2)2 +2 Question no. 9 If the functions f is defined by then find the range of f. Solution: Since x ≤ 5 ,1/x ≥ 1/5.. i.e., f(x) ≥ 1/5. Question no. 10 If the functions f and g are defined by then Calculate gf(2). Solution: gf(x) = g(f(x)) = g(3/x) = 5(3/x) – 1 = (15/x) – 1. So, gf(2) = (15/2) – 1 =13/2 Question no. 11 If the functions g is defined by then find an expression in terms of x for .
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