Answer: A.
The point on the graph of f⁻¹ (x) is (-5,4)
Step-by-step explanation
Let f(x) = -(5/4)x.
This function passes through (4, -5) as specified, because
f(4) = -(4/5)*(4) = -5
Construct f⁻¹ (x) as follows:
Set y = f(x).
y = -(4/5)x
Switch x and y.
x = -(4/5)y
Solve for y
y = -(5/4)x
Set f⁻¹ (x) to y.
f⁻¹ (x) = - (4/5)x.
Test x=-5 to see if y=4.
f⁻¹ (-5) = -(4/5)*(-5) = 4 Correct!