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find the quadratic polynomial whose sum and product of zeros are radic2 1 1 radic2 1ans sum 2 radic2product 1qp x2 - sum x
there are two forms of the parabola which we will be looking at the first form will make graphing parabolas very simple unluckily most parabolas
now lets get back to parabolas there is a basic procedure we can always use to get a pretty good sketch of a parabola following it is 1 determine
we have to probably do a quick review of intercepts before going much beyond intercepts are the points on which the graph will cross the x or
the dashed line along with each of these parabolas is called the axis of symmetry every parabola contains an axis of symmetry and as the graph
all parabolas are vaguely u shaped amp they will contain a highest or lowest point which is called the vertex parabolas might open up or down and
given f x 3x - 2 find f -1 x solutionnow already we know what the inverse to this function is as already weve done some work with it though
the process for finding the inverse of a function is a quite simple one although there are a couple of steps which can on occasion be somewhat
here are two one-to-one functions f x and g x if f o g x x
a function is called one-to-one if no two values of x produce the same y it is a fairly simple definition of one-to-one although it takes an instance
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
find the greatest number of 6 digits exactly divisible by 24 15 and 36 ans999720ans lcm of 24 15 36lcm 3 times 2 times 2 times 2 times 3 times 5
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
show that for odd positive integer to be a perfect square it should be of the form8k 1 let a2m1ans squaring both sides we get a2 4m m 1 1there4
show that the product of 3 consecutive positive integers is divisible by 6ansnn1n2 be three consecutive positive integerswe know that n is of the
if d is the hcf of 30 72 find the value of x amp y satisfying d 30x 72yans5 -2 not uniqueans using euclids algorithm the hcf 30 7272
show that 571 is a prime numberans let x571rarrradicxradic571now 571 lies between the perfect squares of 232 and 242prime numbers
find the least number that is divisible by all numbers between 1 and 10 both inclusiveans the required number is the