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?)
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
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.