Question

Keith used the following steps to find the inverse of f, but he thinks he made an error.

f(x)=7x+5

Answer 1

The inverse of f(x) = 7x + 5 is f^(-1)(x) = (x - 5) / 7.

Step-by-step explanation:

To find the inverse of a function, we need to switch the roles of the input variable, x, and the output variable, f(x), and solve for x.

So, let's start with the equation f(x) = 7x + 5.

Step 1: Replace f(x) with y: y = 7x + 5.

Step 2: Swap x and y: x = 7y + 5.

Step 3: Solve for y:

x = 7y + 5 ⇒ x - 5 = 7y ⇒ (x - 5) / 7 = y.

So, the inverse of f(x) = 7x + 5 is f^(-1)(x) = (x - 5) / 7.