Question

Which function is equivalent to the inverse of y=sec(x)

a. y=cot^-1(x)
b. y=cos^-1(1/x)
c. y=csc^-1(x)
d. y=sin^-1(1/x)

Answer 1

Answer: B) csc^-1(x)

Step-by-step explanation: EDGE 2021

Answer 2

From the identity:


`sec(x)= (1)/(cos(x))`



`f(x)=sec(x)= (1)/(cos(x))`

the inverse of f is g such that f(g(x))=x,

we must find g(x), such that
`(1)/(cos[g(x)])=x`

thus,
`cos[g(x)]= (1)/(x)`


`g(x)=cos^(-1) ((1)/(x))`


Answer: b. g(x)=cos^-1(1/x)