F(a)=2a F(b)=2b determine F(x)=mx+b Have Final Exam today Please Help

Question

the answer is F(x)=2x,

but I have no idea how to get there.

Help would be greatly appreciated.

Thanks

Answer 1

You can wrute 2 equation based on the given values of the function at x = a and x=b:

2a = ma + b and 2b = mb + b.

Subtract the 2nd equation from the 1st one:

2(a-b) = m(a-b)

If a≠b then m=2.

Substitute m=2 into the 2nd equation:

2b = 2b + b

So b= 0.

The function is F(x)=2x

Note that this is true only if a≠b.