# Thread: Find F-1(X), then state whether F-1(X) is a function

1. ## Find F-1(X), then state whether F-1(X) is a function

I need help solving this problem, can anyone do a step by step guide on how to do this?

Find F-1(X), then state whether F-1(X) is a function.
(The small -1 and 2 represent the powers)

1) F(X) = X2 + 3
(Can you also explain why it is a function?)

2. Originally Posted by Brazuca
I need help solving this problem, can anyone do a step by step guide on how to do this?

Find F-1(X), then state whether F-1(X) is a function.
(The small -1 and 2 represent the powers)

1) F(X) = X2 + 3
(Can you also explain why it is a function?)
Let $\displaystyle y = f(x)$, so you would have $\displaystyle y = x^2 + 3$

to find $\displaystyle f^{-1}(x)$, switch $\displaystyle x$ and $\displaystyle y$ in the above equation and solve for $\displaystyle y$, that will give you $\displaystyle f^{-1}(x)$

Remember the definition of a function: it is a relation in which EVERY element in the domain maps to one AND ONLY ONE element in the range

3. Originally Posted by Jhevon
Let $\displaystyle y = f(x)$, so you would have $\displaystyle y = x^2 + 3$

to find $\displaystyle f^{-1}(x)$, switch $\displaystyle x$ and $\displaystyle y$ in the above equation and solve for $\displaystyle y$, that will give you $\displaystyle f^{-1}(x)$

Remember the definition of a function: it is a relation in which EVERY element in the domain maps to one AND ONLY ONE element in the range
In the end I got "Y = (square root of X - 3)"

Now how do I know it is a function?

4. Originally Posted by Brazuca
In the end I got "Y = (square root of X - 3)"

Now how do I know it is a function?
what are the x's in the domain? is each x associated with only one y? if yes, then it is a function. you can do the vertical line test here on the graph as an illustration

5. Originally Posted by Jhevon
what are the x's in the domain? is each x associated with only one y? if yes, then it is a function. you can do the vertical line test here on the graph as an illustration
So would that mean a yes or a no for this? "Y = (square root of X - 3)"

On another problem I got "Y = (cube root of X + 4) - 2" and the answer was yes, but I still don't understand why.

6. Originally Posted by Brazuca
So would that mean a yes or a no for this? "Y = (square root of X - 3)"

On another problem I got "Y = (cube root of X + 4) - 2" and the answer was yes, but I still don't understand why.
as i said, you can do the vertical line test on the graphs. if any vertical line cuts the graph only once, it is a function.

also, try to see if each x gives only one y. it is almost clear that these functions do.

for instance, how do we know that x^2 + y^2 = 1 is not a function. because for x = 0, the value of the function can be +1 or -1. so we have one x giving two values.