What is the function f(x)=(m-1)x+2 if the point (m,4) is on the graph of function, m<2?

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To determine the function, we'll have to find out the leading coefficient of the function.

Since the point (m,4) lies on the graph of function, then it's coordinates verify the expression of the function.

4 = (m-1)m + 2

We'll remove the brackets:

4 = `m^(2)` - m + 2

We'll subtract 4 both sides:

`m^(2)` - m - 2 = 0

We'll apply quadratic formula:

`m_(1,2)` = (-1`+-` `sqrt(1 + 8)` )/2

`m_(1,2)` = (-1`+-` 3)/2

m1 = 1 and m2 = -2

Since both values of m are smaller than 2, but m = 1 makes the function to degenerate, then the only possible value for m is -2 and the function is f(x) = -3x + 2.

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