Let fx and gx be two bijective functions- where fx-3x-5 and gx-ex3-2 - then fogx-1 is equal to

Given: f(x)=3x+5 and g(x)=e^x3 2 ⇒ fog(x)=e^x 6+5 ⇒ fog(x)=e^x 1 Let y=(fog(x))=e^x 1 ⇒ 1+y = e^x ⇒ x=ln(1+y) Replace x with y, we get (fog(x))^ 1=ln(1+x) ...

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Standard XII

Mathematics

Sequence

Let fx and gx...

Question

Let $f (x)$ and $g (x)$ be two bijective functions, where $f (x) = 3 x + 5$ and $g (x) = \frac{e^{x}}{3} - 2$ , then $(f o g (x))^{- 1}$ is equal to

ln x

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ln (1 - x)

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ln (1 + x)

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e^{x} + 1

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Solution

The correct option is C $ln (1 + x)$
Given: $f (x) = 3 x + 5$ and $g (x) = \frac{e^{x}}{3} - 2$
$\Rightarrow f o g (x) = e^{x} - 6 + 5 \Rightarrow f o g (x) = e^{x} - 1$
Let $y = (f o g (x)) = e^{x} - 1$
$\Rightarrow 1 + y = e^{x} \Rightarrow x = ln (1 + y)$
Replace $x$ with $y$ , we get
$(f o g (x))^{- 1} = ln (1 + x)$

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Standard XII Mathematics

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Let f(x) and g(x) be two bijective functions, where f(x)=3x+5 and g(x)=ex3−2 , then (fog(x))−1 is equal to

The correct option is C ln(1+x)Given: f(x)=3x+5 and g(x)=ex3−2 ⇒fog(x)=ex−6+5⇒fog(x)=ex−1 Let y=(fog(x))=ex−1 ⇒1+y=ex⇒x=ln(1+y) Replace x with y, we get (fog(x))−1=ln(1+x)

Let $f (x)$ and $g (x)$ be two bijective functions, where $f (x) = 3 x + 5$ and $g (x) = \frac{e^{x}}{3} - 2$ , then $(f o g (x))^{- 1}$ is equal to