The composite functions when evaluated are
Maximum value of h⁻¹ = 5
h(k(3)) = -4
k⁻¹(h(-3)) = 4
h⁻¹(k⁻¹(3)) = -3
How to evaluate the composite function
From the question, we have the following parameters that can be used in our computation:
The table and the graph
From the graph, we have the maximum to be at
h(5) = 4
When inverted, we have
h⁻¹(4) = 5
This means that the maximum value of h⁻¹ is 5
Next, we have
h(k(3))
From the table, the value of k(3) is
k(3) = -3
This means that
h(k(3)) = h(-3)
Evaluate
h(k(3)) = -4
Next, we have
k⁻¹(h(-3))
This gives
k⁻¹(h(-3)) = k⁻¹(-4)
Evaluate from the table
k⁻¹(h(-3)) = 4
Lastly, we have
h⁻¹(k⁻¹(3))
Evaluate from the table
h⁻¹(k⁻¹(3)) = h⁻¹(-4)
Evaluate from the graph
h⁻¹(k⁻¹(3)) = -3
Hence, the value of h⁻¹(k⁻¹(3)) is -3