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).

Answer 1

Given:

f(x) = 2x − 3

g(x) = x³ + 5

(fog)(x)=f[g(x)]            

=f(x³+5)            

=2(x³+5)−3            

=2x³+10−3            

=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: R→R be defined by `(fog)^-1 (x)=((x-7)/2)^(1/3)`