Question

If f(x)=2x+sin(x) and the function g is the inverse of f, then g'(2)=??
a. 0.40
b. 0.38
c. 0.34
d. 0.32
e. 0.36

Answer 1

There is no inverse for this function.

Answer 2

because it does not pass the vertical line test. for every value of g there are multiple values of x because sin x is the same for many x values.

Answer 3

y = 2 x + sin x
if there were an inverse it would be
x = 2 y + sin y
1 = 2 dy/dx - cos x dy/dx
1 = dy/dx (2-cos x)
dy/dx = 1/(2-cos x)
at x = 2
dy/dx = 1/(2-cos 2) = 1/(2 +.416)
= .41