SOLUTION: What is the inverse of f(x) = (x - 5)^2 for x ≥ 5 where function g is the inverse of function f? The equation and answer choices are in the link here: https://prnt.sc/le3i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What is the inverse of f(x) = (x - 5)^2 for x ≥ 5 where function g is the inverse of function f? The equation and answer choices are in the link here: https://prnt.sc/le3i      Log On


   

Question 1127951: What is the inverse of f(x) = (x - 5)^2 for x ≥ 5 where function g is the inverse of function f?
The equation and answer choices are in the link here: https://prnt.sc/le3ih1
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the inverse of f%28x%29+=+%28x+-+5%29%5E2 for x+%3E=+5
since f%28x%29+=+y
y=+%28x+-+5%29%5E2 swap x and y
x=+%28y+-+5%29%5E2........solve for y
sqrt%28x%29=+sqrt%28%28y+-+5%29%5E2%29
sqrt%28x%29=+y+-+5
sqrt%28x%29%2B5=+y+
so,function g is the inverse of function+f we have
g%28x%29=sqrt%28x%29%2B5 for x+%3E=+5

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The response by the other tutor showed a general method for finding an inverse function: switch the x and y variables and solve for the new y.

Here is different method which is much faster and much less work for many simple functions, including this one.

This method is based on the idea that an inverse function "gets you back where you started". For relatively simple functions, that just means doing the opposite operations in the opposite order.

For the given function, the order of operations is

(1) subtract 5; and
(2) square

The opposite operations, in the opposite order, are

(1) take the square root; and
(2) add 5

So the inverse function is

sqrt%28x%29%2B5