Show that the given function is one-to-one and find its inverse. Check your answ
ID: 2881369 • Letter: S
Question
Show that the given function is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of f is the domain of f inverse and vice-versa. F(x) = 7x - 9 Show that the given function is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of f is the do num of f inverse and vice-versa. F(x) = 8 - 3 squareroot x - 2 Analytically show that the function f (x) = 10 - 3 squareroot x - 5 is one-to-one. find it. inverse, and evaluate the following f^-1(8) f^-1(12) f^-1(7)Explanation / Answer
3)
a)function one-to one or not?
A function f(x) is one to one if, for a and b in it's domain, f(a) = f(b) implies that a = b
f(x)=7x-9
let f(y)=7y-9
f(x)=f(y)
7x-9=7y-9
7x-9+9=7y
7x=7y
divide by 7 to both sides,
x= y
hence function f(x) is one to one function.
b)
y=7x-9 as it is one to one function,
x=7y-9
x+9=7y
y=(x+9)/7
f-1(x)= (x+9)/7 inverse function of f(x)
c)
Now we will verify algebrically,
f(f-1(x))= f-1(f(x))=x or not.
f(f-1(x)) = 7((x+9)/7) -9
=x+9-9
f(f-1(x)) = x
f-1(f(x)) = ((7x-9)+9)/7
=(7x-9+9)/7
=7x/7
f-1(f(x))=x
As f(f-1(x))=f-1(f(x))=x, algebrically inverse function is verified.
d)
range of f is the domain of f inverse
f(x)=7x-9
7x-9=0
x=9/7
so the range is (9/7, infinity)
if f(x)=f(y)
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