To find the inverse of the function f(x) = 2x + 10, we follow a few straightforward steps.
1. **Replace f(x) with y**: We start by rewriting the function as:
y = 2x + 10
2. **Swap x and y**: To find the inverse, we switch x and y, resulting in:
x = 2y + 10
3. **Solve for y**: Next, we need to isolate y. Start by subtracting 10 from both sides:
x – 10 = 2y
Now, divide each side by 2:
y = (x – 10) / 2
4. **Write the inverse function**: Finally, we can express the inverse function as:
f-1(x) = (x – 10) / 2
In conclusion, the inverse of the function f(x) = 2x + 10 is f-1(x) = (x – 10) / 2. This means if you have a value for f(x) and you want to find the corresponding x value, you would use the inverse function.