Question

If f (x) is a linear function such that f (-4)=1 and f (5)=7,2hat is the value of f (1250)?

Answer 1

a/c to question, f(x) is a linear function.

Suppose f(x) = ax + b , where a and b are constant

given, f(-4) = 1

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

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

again, f(5) = 7

f(5) = 5a + b = 7 ........(2)

solve equations (1) and (2),

9a = 6 => a = 2/3 and b = 7 - 5 × 2/3 = 7 - 10/3 = 11/3

hence, f(x) = 2x/3 + 11/3

now, f(1250) = 2 × 1250/3 + 11/3

f(1250) = (2500 + 11)/3 = 2511/3 = 837

hence, f(1250) = 837