Question

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

Answer 1

Answer:

• 9
• (x-8)/3
• -1

Step-by-step 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.

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

A function of its own inverse returns the original value:

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