Question

What is the inverse of the function f(x) = 2x - 10?

1) h(x) = 2x - 5
2) h(x) = 1/2x + 5
3) h(x) = 2x + 5
4) h(x) = 1/2x - 5

Answer 1

The inverse of the function f(x) = 2x - 10 is found by reversing x and y, solving for y, and the correct inverse function is h(x) = 1/2x + 5.

Step-by-step explanation:

To find the inverse of the function f(x) = 2x - 10, swap x and y and solve for y:

• Let y = 2x - 10.
• Swap x and y to get x = 2y - 10.
• Add 10 to both sides to get x + 10 = 2y.
• Divide both sides by 2 to get (x + 10) / 2 = y.
• Rewrite the equation as y = (1/2)x + 5, which is the inverse function.

Therefore, the correct answer is option 2) h(x) = 1/2x + 5.