Let fx be a function defined on -0- 1- such that fx - x x- Q 1-x x- Q- and for all values of x - -0- 1- fofx-a-bx- then the value of a- b is

The correct option is A 1 fof(x)=x, x∈ Q #160; #160; #160; #160; #160; =1 (1 x)=x, x∉ Q #160;Hence fof(x) =x for all valu ...

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Byju's Answer

Standard XII

Mathematics

Properties of Composite Function

Let fx be a f...

Question

Let f(x) be a function defined on [0, 1] such that $f (x) = {\begin{matrix} x & x \in Q 1 - x & x \notin Q \end{matrix}$ and for all values of $x \in [0, 1], f o f (x) = a + b x$ , then the value of $a + b$ is

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Solution

The correct option is A $1$
$f o f (x) = x, x \in Q$

$= 1 - (1 - x) = x, x \notin Q$

Hence $f o f (x) = x$ for all values of $x \in [0, 1]$

Hence $a = 0, b = 1$

So $a + b = 1$

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Let f(x) be a function defined on [0, 1] such thatf(x)={xx∈Q1−xx∉Q and for all values of x∈[0,1],fof(x)=a+bx, then the value of a+b is

The correct option is A 1fof(x)=x,x∈Q =1−(1−x)=x,x∉Q Hence fof(x)=x for all values of x∈[0,1]Hence a=0,b=1So a+b=1

Let f(x) be a function defined on [0, 1] such that $f (x) = {\begin{matrix} x & x \in Q 1 - x & x \notin Q \end{matrix}$ and for all values of $x \in [0, 1], f o f (x) = a + b x$ , then the value of $a + b$ is

The correct option is A $1$
$f o f (x) = x, x \in Q$

$= 1 - (1 - x) = x, x \notin Q$

Hence $f o f (x) = x$ for all values of $x \in [0, 1]$

Hence $a = 0, b = 1$

So $a + b = 1$