Question

A) Find the inverse function of f(x)=2x-7.

B) The graphs of f and f⁻¹ are symmetric with respect to the line defined by y=____

Answer 1

The inverse function of f(x) = 2x - 7 is f⁻¹(x) = (x + 7) / 2. The graphs of f and f⁻¹ are symmetric with respect to the line y = x.

Step-by-step explanation:

To find the inverse function of f(x) = 2x - 7, you swap x and y and then solve for y:

• Let y = 2x - 7.
• Swap x and y to get x = 2y - 7.
• Add 7 to both sides to get x + 7 = 2y.
• Divide both sides by 2 to get y = (x + 7) / 2.

Therefore, the inverse function is f⁻¹(x) = (x + 7) / 2.

The graphs of f and its inverse f⁻¹ are symmetric with respect to the line defined by y = x.