if f(x)=square root of x-4 what is f inverse
I came up with x^2+16
Is f(x) = sqrt(x) - 4 or
is f(x) = sqrt(x - 4)?
If it's the first one then you're correct.
Wait, sorry, my mistake.
If it's the 2nd one then the answer should be x^2 + 4
The 1st one wouldn't be correct. as you would have (y+4)^2 = y^2 + 8y + 16
To find the inverse of a function, we usually switch the roles of x and y in the equation of the function and solve for y.
So, given f(x) = √(x - 4), let's switch x and y:
x = √(y - 4)
Now, let's solve for y:
Square both sides of the equation to get rid of the square root:
x^2 = y - 4
Next, isolate y:
y = x^2 + 4
Therefore, the inverse function of f(x) = √(x - 4) is f^(-1)(x) = x^2 + 4.
So, your answer is correct! The inverse of f(x) is f^(-1)(x) = x^2 + 4.