3 17 Points Given fx v2x a State the domain and range of f b

3. 17 Points] Given fx)- v2x- (a) State the domain and range of f. (b) Verify f is one-to-one. (c) Find the inverse of the function.

Solution

f(x)=(2x-5)

1)2x-5>0

x>5/2

domain =[5/2,)

range =[0,)

2) f(x)=f(b)

(2a-5)=(2b-5)

2a-5=2b-5

2a=2b

a=b

therefore f(x)=(2x-5)is one -to -one function

3)let f(x)=y =>x=f^-1(y)

(2x-5)=y

(2x-5)=y²

x=(y²+5)/2

f^-1(y)=(y²+5)/2

f^-1(x)= (x²+5)/2

d)(fof^-1)x

=f(f^-1(x))

=(2(x²+5)/2 -5)

=((x²+5) -5)

=x²

=x

(f^-1of)x

=f^-1(f(x))

=(((2x-5))²+5)/2

=((2x-5)+5)/2

=2x/2

=x

e) domain =[0,)

range =[5/2,)