Prove that two equations are inverses of each other.

[Physics-Pure]

Homework Statement

f(x) = 9-x^2, x ≥ 0. g(x) = sqrt (9-x)

Homework Equations

Two equations are inverses of each other if f(g(x)) = g(f(x)) = x.

The Attempt at a Solution

f(g(x)) = 9 - (sqrt (9-x))^2

= 9 - (9-x)

 

[voko]

Open the brackets?

 

[Physics-Pure]

Hmm?

 

[Mark44]

Homework Statement

f(x) = 9-x^2, x ≥ 0. g(x) = sqrt (9-x)

Homework Equations

Two equations are inverses of each other if f(g(x)) = g(f(x)) = x.

The Attempt at a Solution

f(g(x)) = 9 - (sqrt (9-x))^2

= 9 - (9-x)

So close! Simplify the above.

Don't forget that you also have to show that g(f(x)) = x.

 

[Mark44]

BTW, we don't normally say that equations are inverses of each other - we say that functions are inverses of each other.