#### Question

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

#### Solution

Given:*f*(*x*) = 2*x* − 3*g*(*x*) = *x*^{3} + 5

(fog)(x)=f[g(x)]

=f(x^{3}+5)

=2(x^{3}+5)−3

=2x^{3}+10−3

=2x^{3}+7

Let (fog)(x)=y

⇒2x^{3}+7=y

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

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

Thus, (fog)^{−}^{1}: R→R be defined by `(fog)^-1 (x)=((x-7)/2)^(1/3)`

Is there an error in this question or solution?

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.