MULTIPLE CHOICE Choose the one alternative that best complet

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the difference quotients f(x +h) f(x) f(x) f(a) for the following function. Rationalize the numerator when and necessary. 6) f(x) x h x-a X h

Solution

f(x) = 4/x

f(x+h) = 4/(x+h) ;

f(a) = 4/a

{ f(x+h) -f(x) } /(h) = { 4/(x+h) -4/x }/h

Taking (x+h)x as common denominator:

= { 4x - 4(x+h) }/(x+h)xh

= -4h/(x+h)xh = -4/(x(x+h)

Now we find { f(x) -f(a) }/(x -a)

= { 4/x - 4/a}/( x-a)

Taking a*x as common denominator:

= 4(a -x)/a*x(x-a)

=- 4/ax

Option C

= 4(a -x)