Question is as below :

$\mathrm{We} \mathrm{find} \mathrm{the} \mathrm{inverse} \mathrm{of} \mathrm{function} f$$\mathrm{Let} y = f\left(x\right)={\left({\mathrm{ax}}^2+b\right)}^3$$y^{1/3}={\mathrm{ax}}^2+b$$y^{1/3}-b={\mathrm{ax}}^2$$\frac{ y^{1/3}-b}{a}=x^2$$x=\sqrt{\frac{ y^{1/3}-b}{a}}$$\mathrm{Hence} g\left(x\right) = \sqrt{\frac{ x^{1/3}-b}{a}} \mathrm{such} \mathrm{that} f\left(g\right(x\left)\right) = g\left(f\right(x\left)\right)$">