Math majors/teachers! Major help needed. College Algebra.?

Question

1 I need an equation for a line that passes through (4,5) and perpendicular to a line that passes through (-1,3) and (2,9). I dont even know how to get started or what to do with any of the coordinates.

#2 Find the domain of (h/g)(x) given that H(x)=5x / 3x-7 and g(x)=X^4-1 / 5x-15 The fifteen is supposed to have the composition sign after it... Didnt know how to type it in..

#3 Given f(x)=4x^3-5x find each of the following! a)... f(2) b)... f(-2) c)... f(a) d)... f(-a) Do I just put the #s in for all three x's in the problem? Or just the two that come AFTER the = sign?

Answer 1

1) use y=mx+b there m is the slope of the line you are looking for.  The slope of a perpendicular line is 1/a where a is the slope of the original line( the line that goes through (-1,3) and (2,9).  To find a, use slope = (y2-y1)/(x2-x1) and input the coordinates you are given.  Then divide 1 by that answer and that is your slope (m).  Now you are given x and y for your line, which must go through 4,5 therefore you have m, x and y so find b and that's your equation.

2)the domain is all values of x for which this function is defined.  The function (h/g)(x) is equal to h(x)/g(x) which is (5x/(3x-7))/(x^4 -1/(5x-15)) = (5x(5x-15))/((3x-7)(x^4 -1)).  So any value of x for which the denominator is not zero is the domain (so set each part ...ie 3x-7 and x^4 -1...of the denominator equal to zero separately and solve for x).

3)input the numbers as they are, so find the answer if x=2, -2, a and -a.  Don't forget that a negative times a negative is positive and a negative times a positive is negative (that's the trick here).  

Answer 2

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