Question

Plsss help

A table of values for f(x) is given. Find a table, a graph, and an equation for f-¹(x). Assume f(x) is continuous.
X : 2, 3, 4, 5, 6
Y: -1 ,0, 3, 8, 15
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Answer 1

Hello,

Explanation:

I don't know the school's method but i have found this one.

`\begin{array}cx&y&\Delta^1&\Delta^2\\--&--&--&--\\-2&-1&&\\3&0&1&\\4&3&3&2\\5&8&5&2\\6&15&7&2\\--&--&--&--\\\end {array}\\\\y=k_1+k_2*x+k_3*x^2\\if\ x=2:\ k_1+2k_2+4k_3=-1\ (1)\\if\ x=3:\ k_1+3k_2+9k_3=0\ (2)\\if\ x=4:\ k_1+4k_2+16k_3=3\ (3)\\\\\\(2)-(1) = > \ k_2+5k_3=1\ (4) \\(3)-(1) = > \ k_2+7k_3=3\ (5)\\\\(5)-(4) = > \ 2k_3=2 = > k_3=1\\k_2=1-5k_3=1-5=-4\\k_1=-1-2k_2-4k_3=-1-2*(-4)-4*1=-1+8-4=3\\\boxed{y=x^2-4x+3}`

Graph: see picture

`\\f^(-1): x=y^2-4y+3\\`