T o convert from X degrees centigrade to y degrees fahrenheit the function is f(x) 9/5x +32 find the inverse function f of negative 1. what does the inverse function represent? graph Help me!
The inverse function simply represents f(-x) and means that you have to flip the x and the y. If that makes sense.
To find the inverse function of f(x) = (9/5)x + 32, we need to find the function that undoes the original function. Let's call the inverse function f^(-1)(x).
To find the inverse function, we'll start by replacing f(x) with y and then solve for x.
y = (9/5)x + 32
Now, we'll swap x and y:
x = (9/5)y + 32
Next, we'll isolate y by subtracting 32 from both sides:
x - 32 = (9/5)y
Now, we'll multiply both sides by 5/9 to isolate y:
(5/9)(x - 32) = y
So, the inverse function is:
f^(-1)(x) = (5/9)(x - 32)
The inverse function represents the conversion from degrees Fahrenheit (x) to degrees Celsius (y). By using the inverse function, you can find the Celsius temperature corresponding to a given Fahrenheit temperature.
To graph the inverse function, you can plot points by substituting x-values into the inverse function and finding the corresponding y-values. Alternatively, you can graph it by reflecting the original function f(x) = (9/5)x + 32 across the line y = x. This means that the x-values of the inverse function become the y-values of the original function, and vice versa.
I hope this helps you understand how to find the inverse function and its meaning. Let me know if you need further assistance!