# Let F Be The Function Given By F(x) = A) Find The

 AnonymousFrom: -Posts: -Votes: - Let f be the function given by f(x) = a) Find the domain of f and determine whether f is an odd or even function. b) Find f l (x) c) Find the slope of the line normal to the graph of f at x = 5.

 FamousAsianFrom: USPosts: 5Votes: 20 F(x) = √(x^4-16x^2) (a) domain is the set of all ALLOWABLE values of x NON-ALLOWABLE values of x are those that make f(x) NOT A REAL NUMBER in this case, f(x) will not be a real number if the quantity under the square root is NEGATIVE, that is: =>any x is allowable EXCEPT x^4-16x^2 < 0 =>which means the same as, any x is allowable if x^4-16x^2 > 0 because x2 is positive, we can divide both sides by x2 without reversing the inequality symbol x2-16 > 0 ----> |x| > 4 ------> -4 > x AND x < 4 -->DOMAIN ----------- odd function means f(-x) = -f(x) even function means f(-x) = f(x) in this case, f(-x) = √((-x)^4-16(-x)^2) = √(x^4-16x^2) = f(x) therefore, f(x) is even --------- (b)using the chain rule f ' (x) = [1/ {2 √(x^4-16x^2)} ] * [4x^3 - 32x] = { 2x^3 - 16x}/ {√(x^4-16x^2)} ------- (c)the slope of the NORMAL at x =5 is the negative reciprocal of the slope of the TANGENT at x = 5 the slope of the TANGENT at x = 5 equals f ' (5) = { 2(5)^3 - 16(5)}/ {√((5)^4-16(5)^2)} = 34/3 therefore, the slope of the NORMAL at x =5 is -3/34

 AnonymousFrom: -Posts: -Votes: - For a given function f(x) a) the domain is all the values of x for which f(x) gives a finite value if f(x)=-f(-x) then function is odd if f(x)= f(-x) then the function is even b) just differentiate the given function wrt x in usual way to get f1(x) c) f1(5) gives the slope of the tangent -(1/f1(5)) gives the slope of the normal line plz rate the best answer first..

 LondonBrainFrom: USPosts: 8Votes: 32 F(x)= ?