Given that f(x) =is one-to- one, find each of the following: a) find , the equation of the inverse of f(x) =b) find the coordinates of f (x )andc) find the domain and range of both f(x) and

a) Since the function is given to be one - one so the inverse of the function exist. Now f(x) maps x to y so the inverse of f(x) maps y to x

To find inverse, first interchange the roles of x and y :

Now, solve for y :

b) To find coordinates of f(x) :

First take y = 0 then take x = 0

⇒ x-coordinates : (-125,0) and y-coordinates : (0,5)

To find coordinates of inverse function of x :

First take y = 0 then take x = 0

⇒ x - coordinates : (5,0) and y - coordinates : (0,-125)

c)  f(x) is defined for every real number.

⇒ Domain : -∞ < x < ∞

and Range : -∞ < f(x) < ∞

And inverse function of x is also defined for every real number :

⇒ Domain : -∞ < x < ∞

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step-by-step explanation:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!