If f:IR to IR is defined by f(x) = 3x - 4 , then {f^{ - 1}}:IR to IR is

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1.Relation and Function

easy

If $f:IR \to IR$ is defined by $f(x) = 3x - 4$, then ${f^{ - 1}}:IR \to IR$ is

A

$4 - 3x$

B

$\frac{{x + 4}}{3}$

C

$\frac{1}{{3x - 4}}$

D

$\frac{3}{{x + 4}}$

Solution

(b) Given $f(x) = 3x – 4$.

Now let $y = {f^{ – 1}}(x)\,\, \Rightarrow \,\,f(y) = x$

$ \Rightarrow \,\,3y – 4 = x\,\, \Rightarrow \,\,3y = x + 4$

$ \Rightarrow \,\,y = \frac{{x + 4}}{3}\,\, $

$\Rightarrow \,\,{f^{ – 1}}(x) = \frac{{x + 4}}{3}$.

Standard 12

Mathematics

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