Find the inverse of the function $$f(x)=\sqrt{x}+6$$

Question

anonymous · Answer

Rearrange so

x=f(x)/6

then invert

f^-1(x)=x/6

bahrom7893 · Answer

Wrong

bahrom7893 · Answer

replace f(x) by x and x by f(x) and solve for f(x)

bahrom7893 · Answer

x=sqrt(f(x)) + 6

bahrom7893 · Answer

Solve for f(x)

anonymous · Answer

An inverse function in this case will be something that turns $$\sqrt{x}+6 \rightarrow x$$

bahrom7893 · Answer

x-6=sqrt(f(x))
inverse is:
f^-1(x) = (x-6)^2

anonymous · Answer

In comparison to the normal function:$$x \rightarrow \sqrt{x}+6$$

anonymous · Answer

@bahrom7893 does this method work for finding all inverse functions?

bahrom7893 · Answer

well i've always used it. Idk of any exceptions.

bahrom7893 · Answer

bahrom7893 · Answer

oh it does... but i showed u the steps in reverse...

bahrom7893 · Answer

When you have an equation, solve for x. You'll get:
x = y+sqrt(y) or something.. <-- I made that up, so the inverse will be:
f^-1(x) = x+sqrt(x)

anonymous · Answer

your hella cool. thanks.

bahrom7893 · Answer

anonymous · Answer

let y= sqrt(x)+6
4y-6=sqrt(x)
x=(4y-6)^2
replace x by  inverse (x) and y by x,
therefore inverse(x)= (4x-6)^2