Final answer:
The inverse function of f(x)=2x−5 is found by swapping x and y, resulting in the inverse function f⁻¹(x) = ½(x + 5).
Step-by-step explanation:
To find the inverse function of f(x)=2x−5, we need to solve for 'x' in terms of 'y'. Let's start by replacing f(x) with y:
y = 2x − 5
Now, we switch x and y to find the inverse function:
x = 2y − 5
Next, we solve for y:
x + 5 = 2y
½(x + 5) = y
Thus, the inverse function, denoted as f⁻¹(x), is:
f⁻¹(x) = ½(x + 5)
This demonstrates how subtraction and division are inverse operations to addition and multiplication, respectively.