Question

Write the equation of a linear function f, such that f(1)=4 and f(4)=1 Then find f(-2)

Answer 1

If f(x) is a linear function, then

f(x) = ax + b

for some constants a and b.

Given that f (1) = 4 and f (4) = 1, these constants are such that

f (1) = a + b = 4

f (4) = 4a + b = 1

Solve for a and b : eliminate b by subtracting the two equations,

(a + b) - (4a + b) = 4 - 1

-3a = 3

a = -1

Then

-1 + b = 4

b = 5

So we have

f(x) = -x + 5