find the inverse of q(x)=(x-5)^2
To find the inverse of a function, we need to exchange the roles of x and y and solve for y. Let's start with the given function q(x) = (x - 5)^2.
Step 1: Replace q(x) with y.
y = (x - 5)^2
Step 2: Swap x and y.
x = (y - 5)^2
Step 3: Solve the equation for y.
Take the square root of both sides to eliminate the square:
√x = y - 5
Step 4: Isolate y by adding 5 to both sides of the equation.
√x + 5 = y
Now, we have the equation for the inverse function:
q^(-1)(x) = √x + 5
Therefore, the inverse of q(x) = (x - 5)^2 is q^(-1)(x) = √x + 5.