Algebra Answers

f:x ----> 3-4x-x^2, x<c
g:x ----> ln (3-x), x<3

1. find the range of the function f when c =0
2. find the largest value of c for which the composite function gf is defined.

f:x ----> 3-4x-x^2, x<c
g:x ----> ln (3-x), x<3

find an expression for g^-1(x)

Use the Factor Theorem to find the linear factors of 2x^3 - 9x^2 -2x +24

3x^2+1 > |x-3|

(x^3 + y^3 +z^3 - 3xyz)= (x+y+z) (x+wy +w^2 z)(x+w^2 y+wz)
W is omega

1.Find the values of a and b in each of the following:
i) (5+2√3) / (7+4√3) = a−6√3
ii) (3−√5) / (3+2√5) = a√5−9/11
iii) (√2+√3) / (3√2−2√3) = 2−b√6
iv) (7+√5) / (7−√5) - (7−√5) / (7+√5) = a+7/11√5 b

2.If a=2+√3, then find the value of a - 1/a

3.If a=3+√5 / 2, then find the value of a^2 + 1/a^2

4.Simplify: (7√3) / (√10 + √3) - (2√5) / (√6 +√5 ) - (3√2) / (√15 + 3√2)

1) if (√5−1)/(√5+1)+(√5+1)/(√5−1)=a+b√5 , find a and b .
2) Simplify : 1/(1+√2−√3) by rationalising the denominator.

(a^2-a)^2-8(a^2-a)+20

x² -10x + 33 ≡ (x - a)² + b

Work out the value of a and the value of b

What is the minimum value of x² - 10x + 33?

Let V be the subspace of P3 spanned by the the following set
{1-x^2+x^3 , 2+x-x^2+x^3 , 1+2x+x^2-x^3}

(a) Show that f(x) = x + x^2 - x^3 ∈ V .
(b) Show that g(x) = 1 + x - x^2 +x^3 is not an element of V .
(c) Find a basis for V which contains f(x).
(d) Find a basis for P3 which contains g(x).