Answer:
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 < ∞