HSC Science (Computer Science) 11thMaharashtra State Board
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If the function f : R → R be defined by f(x) = 2x − 3 and g : R → R by g(x) = x3 + 5, then find the value of (fog)−1 (x). - HSC Science (Computer Science) 11th - Mathematics and Statistics

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Question

If the function f : R → R be defined by f(x) = 2x − 3 and g : R → R by g(x) = x3 + 5, then find the value of (fog)−1 (x).

Solution

Given:

f(x) = 2x − 3

g(x) = x3 + 5

(fog)(x)=f[g(x)]            

=f(x3+5)            

=2(x3+5)3            

=2x3+103            

=2x3+7

Let (fog)(x)=y

2x3+7=y

`=>x=((y-7)/2)^(1/3)`

`=>(fog)^-1 (y)=((y-7)/2)^(1/3)`

Thus, (fog)1: RR be defined by `(fog)^-1 (x)=((x-7)/2)^(1/3)`

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Solution If the function f : R → R be defined by f(x) = 2x − 3 and g : R → R by g(x) = x3 + 5, then find the value of (fog)−1 (x). Concept: Composition of Functions and Invertible Function.
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