Determine whether the given function is onetoone If it is on

Determine whether the given function is one-to-one. If it is one-to-one, find a formula for the inverse. f(x) = squareroot x - 7 f^-1(x) = squareroot x + 7 f^-1(x) = x^2 + 7, x greaterthanorequalto 0 Not one-to-one f^-1(x) = (x - 7)^2

Solution

f(x)=sqrt(x-7)

here for every value of x we have a value for y so its one to one.

Lets find the inverse

first we have to write f(x)=y and then switch x and y

y=sqrt(x-7)

x=sqrt(y-7)

x^2=y-7

y=x^+ 7, x>=0