Question

To one-one functions g and h are defined as follows.

Answer 1

• 9
• (x-8)/3
• -1

Explanation:

The inverse function for a set of ordered pairs can be found by swapping the x- and y-coordinates in each pair.

`g^(-1)(-1)=9\qquad\text{from the $g(x)$ ordered pair $(9, -1)$}`

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The inverse of a function expressed algebraically can be found by swapping the x- and y-variables and solving for y.

`h^(-1)(x)\qquad\text{is found from }x=h(y)\\\\x=3y+8\\x-8=3y\\\\y=(x-8)/(3)\\\\\boxed{h^(-1)(x)=(x-8)/(3)}`

A function of its own inverse returns the original value:

`\boxed{\left(h\circ h^(-1)\right)(-1)=-1}`