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in previous section we looked at the two functions f x 3x - 2 and g x x3 23 and saw
given fx 23x-x2 and gx 2x-1 evaluate fg x fogx and gof xsolutionthese are the similar functions that we utilized in the first set of
we have to note a couple of things here regarding function composition primary it is not multiplication regardless of what the notation may
now we need to discuss the new method of combining functions the new way of combining functions is called function composition following is the
given f x 2 3x - x2 and g x 2 x -1 evaluate f g 4solutionthrough evaluate we mean one of two things based on what is in the
the topic along with functions which we ought to deal with is combining functions for the most part this means performing fundamental arithmetic
now we need to discuss graphing functions if we recall from the earlier section we said thatf x is nothing more than a fancy way of writing y it
find out the domain of each of the following functionsg x x3 x2 3x -10solutionthe domain for this function is all of the values of x for which we
domain and rangethe domain of any equation is the set of all xs which we can plug in the equation amp get back a real number for y the range of any
given f x x2 - 2 x 8 and g x radicx 6 evaluate f 3 and g3solutionokay weve two function evaluations to do here and weve also obtained
coordinates for the point the listed first number is the x-coordinate of the point and the second number listed is the y-coordinate of the point
graphing and functions graphingin this section we have to review some of the fundamental ideas in graphing it is supposed
solve following 3x 2 lt 0solutionnow we know that p ge 0 and thus cant ever be less than
solve following2x - 3 7solutionagain p represents the quantity within the absolute value bars thus all we have to do here is plug into the formula
inequalities involving gt and geonce again lets begin along a simple number
solve following 2 x - 4 10solutionthere actually isnt much to do other than plug into the formula as with equations p merely represents
in the earlier section we solved equations which contained absolute values in this section we desire to look at inequalities which contain
example solve following 10 x - 3 0 solutionlets approach this
solve following 2x -
in the last two sections of this chapter we desire to discuss solving equations amp inequalities that have absolute values we will look at
in this section we are going to solve inequalities which involve rational expressions the procedure for solving rational inequalities is closely
examples of polynomial that doesnt factornow all of the examples that weve worked to this point comprised factorable polynomials however that
now it is time to look at solving some more hard inequalities in this section we will be solving single inequalities which involve polynomials of
solve out following inequalities give both inequality amp interval notation forms for the solution -14 lt -7 3x 2 lt