Question

If f(x) = mx+n, where m and n . are integers
f (-2) = 7 and f(3) = 2, then m and n are equal to

Answer 1

Answer:

For a limit to exist there should exist both left hand limit and right hand limit and both limits must be equal

For

x→0

lim

f(x) to exist, the condition is;

x→0

+

lim

f(x)=

x→0

−

lim

f(x)=f(0)

Applying above conditions for

x→0

lim

, we get

m(0)+n=n(0)+m

⇒m=n ...... (1)

Applying similar condition for

x→1

lim

we get ;

n(1)+m=n(1

3

)+m

⇒n+m=n+m which is always true

For both the limits to exist, m must be equal to n

∴m=n