Question

4
type the correct answer in each box.

functions h and k are inverse functions, and both are defined for all real numbers.
using this relationship, what is the value of each function composition?

$(h \circ k)(3) = \square$
$(k \circ h)(-4b) = \square$

Explanation:

Step1: Recall inverse function property

For inverse functions \(h\) and \(k\), \((h \circ k)(x) = h(k(x)) = x\) for all real \(x\).

Step2: Evaluate \((h \circ k)(3)\)

Substitute \(x=3\) into the property:
\((h \circ k)(3) = 3\)

Step3: Evaluate \((k \circ h)(-4b)\)

For inverse functions, \((k \circ h)(x) = k(h(x)) = x\) for all real \(x\). Substitute \(x=-4b\):
\((k \circ h)(-4b) = -4b\)

Answer:

\((h \circ k)(3) = 3\)
\((k \circ h)(-4b) = -4b\)