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The equation defines a one-to-one...

The equation defines a one-to-one function f.

f(x) = 9x − 1

Determine

f −1.f −1(x) =Verify that

f ∘ f −1

and

f −1 ∘ f

are both the identity function.

(f ∘ f −1)(x) = f(f −1(x))= f= 9− 1= − 1= x(f −1 ∘ f)(x) = f −1(f(x))= f −1=+ 1

9=

9= x

f(x) = 9x − 1

Determine

f −1.f −1(x) =Verify that

f ∘ f −1

and

f −1 ∘ f

are both the identity function.

(f ∘ f −1)(x) = f(f −1(x))= f= 9− 1= − 1= x(f −1 ∘ f)(x) = f −1(f(x))= f −1=+ 1

9=

9= x

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