Question

The function f(x) = 5x + 7 is one-to-one.

Find an equation for f⁻¹ the inverse function.

Answer 1

To find the inverse function of f(x) = 5x + 7, switch x and y, solve for y, and rewrite the equation as f⁻¹(x) = (x - 7)/5.

Step-by-step explanation:

To find the inverse function, we need to switch the roles of x and y in the original function and solve for y.

The original function is f(x) = 5x + 7. Let's replace f(x) with y.

y = 5x + 7

To find the inverse, we switch x and y:

x = 5y + 7

Now, solve this equation for y:

Subtract 7 from both sides: x - 7 = 5y

Divide both sides by 5: (x - 7)/5 = y

So, the equation for the inverse function is f⁻¹(x) = (x - 7)/5.