Question

What is the inverse function of f(x)=2x−5?

Answer 1

Step-by-step explanation:

`f(x)=2x-5\\x=(f(x)+5)/(2)\\f^(-1)(x)=(x+5)/(2)`

Answer 2

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.