Let f x 7x squareroot x 50 Choose the form of the largest

Let f (x) = 7x + squareroot x + 50. Choose the form of the largest interval on which f has an inverse and enter the value(s) of the endpoint(s) in the appropriate blanks. Then find (f^-1)\'(0). Enter DNE in any unused answer blank) (-infinity/infinity)) (-v, b)) (-infinity, b] (a, b) (a, b] [a, b) [a, b] (a, infinity) [a, infinity)

Solution

[a,)

a =-50,

b=

f(x)=7x+(x+50)

f \'(x)=7+ (1/(2(x+50)))

f(-1)=0

f ^-1(0)=-1

f(f ^-1(x))=x

differentiate

f \'(f ^-1(x))(f ^-1(x))\'=1

(f ^-1(x))\'=1/f \'(f ^-1(x))

(f ^-1(0))\'=1/f \'(f ^-1(0))

(f ^-1(0))\'=1/f \'(-1)

(f ^-1(0))\'=1/[7+ (1/(2(-1+50)))]

(f ^-1(0))\'=1/[7+ (1/14)]

(f ^-1(0))\'=14/99