Fx - - 5- x- 2- ax-b- 2 10 -If f3-5 f5-3Find a-b

f(3)=5 3a+b=5⋯(1) f(5)=3 5a+b=3⋯(2) (2) (1) 5a+b 3a b=3 5 2a= 2 a= 1 b 3=5 b=8 ...

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Byju's Answer

Standard XII

Mathematics

Theorems for Continuity

fx = [[ ...

Question

$f (x)$ = $[\begin{matrix} 5, & x \leq 2 a x + b, & 2 < x < 10 21, & x > 10 \end{matrix}$
If $f (3) = 5 f (5) = 3$
Find $a, b$

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Solution

$f (3) = 5 3 a + b = 5 \dots (1) f (5) = 3 5 a + b = 3 \dots (2) (2) - (1) 5 a + b - 3 a - b = 3 - 5 2 a = - 2 a = - 1 ⟹ b - 3 = 5 b = 8$

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Similar questions

Q. Let

f (x) = | x - 1 | + | x - 2 | .

Then which of the following is/are true?

Q. For the functions

f (x) = a x + b

f (- 1) = - 5

and

f (3) = 3

f i n d

(a - b) .

Q. If

f (x) = \{\begin{cases} a x^{2} - b, & if |x| < 1 \\ \frac{1}{|x|}, & if |x| \geq 1 \end{cases}

is differentiable at x = 1, find a, b.

$(a) P r o v e t h a t \int_{0}^{2 a} f (x) d x = 2 \int_{0}^{a} f (X) d x, i f f (2 a - x) = f (x) a n d e v a l u a t e \int_{0}^{2 π} c o s^{5} x d x$
$i f f (2 a - x) = - f (x)$

(b) Find the values of a and b such that the function defined by

$f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 5, & i f x \leq 2 a x + b & i f 2 < x < 10 i s a c o n t i n o u s f u n c t i o n 21, & i f x \geq 10 \end{matrix}$

Q. If

f (x) = \{\begin{matrix} x^{2}, & when x < 0 \\ x, & when 0 \leq x < 1 \\ \frac{1}{x}, & when x \geq 1 \end{matrix}

find: (a) f(1/2), (b) f(−2), (c) f(1), (d)

f (\sqrt{3})

and (e)

f (\sqrt{- 3})

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f(x) = [5,x≤2ax+b,2<x<1021,x>10If f(3)=5f(5)=3Find a,b

f(3)=53a+b=5⋯(1)f(5)=35a+b=3⋯(2)(2)−(1)5a+b−3a−b=3−52a=−2a=−1⟹b−3=5b=8

$f (x)$ = $[\begin{matrix} 5, & x \leq 2 a x + b, & 2 < x < 10 21, & x > 10 \end{matrix}$
If $f (3) = 5 f (5) = 3$
Find $a, b$

$f (3) = 5 3 a + b = 5 \dots (1) f (5) = 3 5 a + b = 3 \dots (2) (2) - (1) 5 a + b - 3 a - b = 3 - 5 2 a = - 2 a = - 1 ⟹ b - 3 = 5 b = 8$