for the function f(x)=(3-4x)^2, find f-1. determine whether f-1 is a function
since f is a parabola, there are two values of x for each value of y.
So, f^-1 cannot be a function.
f^-1(x) = (3-√x)/4
thanks for the help
To find the inverse of the function f(x) = (3-4x)^2, we need to follow these steps:
Step 1: Replace f(x) with y, so we have the equation: y = (3-4x)^2.
Step 2: Swap the x and y variables: x = (3-4y)^2.
Step 3: Solve the equation for y. Start by taking the square root of both sides:
√x = 3-4y.
Step 4: Isolate y on one side by rearranging the equation:
4y = 3 - √x.
Step 5: Divide both sides of the equation by 4:
y = (3 - √x) / 4.
So, the inverse of the function f(x) = (3-4x)^2 is f^(-1)(x) = (3 - √x) / 4.
Now, to check if f^(-1) is a function, we need to make sure that for every value of x in the domain of f(x), the inverse function f^(-1)(x) gives us exactly one y-value.
For f(x) = (3-4x)^2, the domain is all real numbers. So, for every x, we should have a unique y-value.
In the inverse function f^(-1)(x) = (3 - √x) / 4, we can see that the domain is also all real numbers (assuming x ≥ 0 since we have a square root of x). And for each x, we have a single corresponding y-value.
Hence, the inverse function f^(-1) is a function.