Explanation:
Inverse of a Function.
To find the inverse of the function f(x) = √(x+7), we need to interchange the roles of x and y and solve for y.
Let y = f(x) = √(x+7)
To find the inverse, we need to solve for x in terms of y.
Step 1: Square both sides of the equation to eliminate the square root:
y^2 = x + 7
Step 2: Solve for x:
x = y^2 - 7
So the inverse of the function f(x) is:
f^(-1)(y) = y^2 - 7
We can also express the inverse in terms of x:
f^(-1)(x) = x^2 - 7
Note that we changed the variable from x to y, and from y to x, when expressing the inverse function.