If fx-3x-24x-3 for x-34 then fofx is

The correct option is A 17x We have, #10; #10; f( x )=3x+24x 3 for x34 #10; #10; fof( x )=3f( x )+24f( #10;x ) 3 #10; #10; = ...

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Standard XII

Mathematics

Polynomial Functions

If fx=3x+24...

Question

If $f (x) = \frac{3 x + 2}{4 x - 3}$ for $x \neq \frac{3}{4}$ then $f o f (x)$ is

17 x

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3 x

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4 x

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x

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Solution

The correct option is A $17 x$
We have,

$f (x) = \frac{3 x + 2}{4 x - 3} f o r x \neq \frac{3}{4}$

$f o f (x) = \frac{3 f (x) + 2}{4 f (x) - 3}$

$= \frac{3 \frac{3 x + 2}{4 x - 3} + 2}{4 \frac{3 x + 2}{4 x - 3} - 3}$

$= \frac{9 x + 6 + 8 x - 6}{12 x + 8 - 12 x + 9}$

$= \frac{17 x}{1}$

$= 17 x$

Hence, this is the answer.

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Similar questions

Question 24
Factorise
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(ii) $x^{3} - 6 x^{2} + 11 x - 6$

(iii) $x^{3} + x^{2} - 4 x - 4$

(iv) $3 x^{3} - x^{2} - 3 x + 1$

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The inverse of the real function f(x) = $\frac{4 x}{3 x + 4}$ , $x \neq \frac{- 4}{3}$ ,is f^-1(x) =

Q. If

f (x) = \frac{4 x + 3}{6 x - 4}, x \neq \frac{2}{3}

, show that

f o f (x) = x

, for all

x \neq \frac{2}{3}

. What is the inverse of

f

Q. If

f (x) = 4 x^{3} + 3 x^{2} + 3 x + 4

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is equal to

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If f(x)=3x+24x−3 for x≠34 then fof(x) is

The correct option is A 17xWe have, f(x)=3x+24x−3forx≠34 fof(x)=3f(x)+24f(x)−3 =33x+24x−3+243x+24x−3−3 =9x+6+8x−612x+8−12x+9 =17x1 =17x Hence, this is the answer.

If $f (x) = \frac{3 x + 2}{4 x - 3}$ for $x \neq \frac{3}{4}$ then $f o f (x)$ is