Question

If f(x) = `("a" - x)/("b" - x)`, f(2) is undefined, and f(3) = 5, find a and b

Answer 1

f(x) = `("a" - x)/("b" - x)`

∴ f(2) = `("a" - 2)/("b" - 2)`

∵ f(2) is not defined

∴ b – 2 = 0

∴ b = 2

Also, f(3) = `("a" - 3)/("b" - 3)`

∵  f(3) = 5

∴ `("a" - 3)/(2 - 3)` = 5    ...[∵ b = 2]

∴ a – 3 = – 5

∴ a = – 2

Hence, a = – 2, b = 2.