If $f (x) = a x + b,$ where, a and b are integers, $f (- 1) = - 5$ and $f (3) = 3,$ then a and b are equal
(a) $a = - 3, b = - 1$
(b) $a = 2, b = - 3$
(c) $a = 0, b = 2$
(d) $a = 2, b = 3$

Q. For the functions

f (x) = a x + b

f (- 1) = - 5

and

f (3) = 3

f i n d

(a - b) .

Q. Suppose

f (x) = a x + b

and

g (x) = b x + a

, where

a

and

b

are positive integers. If

f (g (50)) - g (f (50)) = 28

then the product

(a b)

can have the value equal to

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If f(x)=ax+b, where a and b are integers, f(–1)=–5 and f(3)=3, then a and b are equal to , respectively.

The correct option is D −3f(x)=ax+b f(−1)=−5⇒−a+b=−5 ...[1]f(3)=3⇒3a+b=3 ..[2]Subtracting equation [1] from [2], we get:4a=8⇒a=2∴−2+b=−5⇒b=−3

If $f (x) = a x + b$ , where $a$ and $b$ are integers, $f (- 1) = - 5$ and $f (3) = 3$ , then $a$ and $b$ are equal to , respectively.

The correct option is D $- 3$
$f (x) = a x + b$
$f (- 1) = - 5 \Rightarrow - a + b = - 5 . . . [1] f (3) = 3 \Rightarrow 3 a + b = 3 . . [2] Subtracting equation [1] from [2], we get : 4 a = 8 \Rightarrow a = 2 ∴ - 2 + b = - 5 \Rightarrow b = - 3$