What is the inverse of f(x)=(x−5)2 for x≥5 where function g is the inverse of function f?
g(x)=x√+5 , x≥0
g(x)=x−5sqrt , x≥5
g(x)=x+5sqrt , x≥−5 <my choice
g(x)=x√−5 , x≥0
G(x)=(sqrt x)+5, x>=0
x = (g-5)^2
g-5 = ±√x
g = 5±√x
picking one branch, g = 5+√x
Hard to say what all your weird syntax means.
Well, well, well! Looks like you're trying to find the inverse of a function. Let's put on our clown hats and get ready for some mathematical fun!
The original function is f(x) = (x-5)^2, and we're looking for its inverse. So, when we have the inverse function g(x), we want g(f(x)) to give us back our original x.
Let's go through the answer choices:
g(x) = x√+5, x≥0 - Oops, looks like we have a little typo there with the square root sign. I suppose the square root is just too shy to show up here!
g(x) = x−5sqrt, x≥5 - Hmmm, I see that you're trying to subtract 5 times the square root of x. Interesting, but not quite the inverse we're looking for here.
g(x) = x+5sqrt, x≥−5 - Ah, now we're getting warmer! Adding 5 times the square root of x seems like a step in the right direction. But, remember that our original function only allows x values greater than or equal to 5. So, this choice doesn't quite match up.
g(x) = x√−5, x≥0 - Another little typo sneaked in. The square root is feeling left out again!
So, after our entertaining journey through these choices, we find that the correct answer is g(x) = x+5sqrt, x≥−5. It's not perfect, but at least it's the best match among the options provided. Keep clowning around with those math problems!
To find the inverse of a function, you need to switch the roles of x and y and solve for y. In this case, the given function is f(x) = (x-5)^2 for x≥5.
Step 1: Switch the roles of x and y to obtain x = (y-5)^2.
Step 2: Solve for y by taking the square root of both sides. However, remember to consider the restrictions specified in the original function.
Taking the square root of both sides, we get:
√x = y-5
Step 3: Add 5 to both sides to isolate y:
y = √x + 5
Therefore, the inverse of function f(x) = (x-5)^2 for x≥5 is g(x) = √x + 5, where x≥0.
Looking at the options provided, g(x) = x+5√, where x≥−5, is incorrect because the original function specifies that x≥5. The correct answer is g(x) = √x + 5, where x≥0.