Write $(h \circ f)^{-1}$ when $h(x)= x \ln(3 + x)$ and $f(x) = x^2 − x$

Question

I have arrived up to a point but haven't solved it yet:

$$(h \circ f)^{-1} = y= (x ^2 − x )· \ln(3 + x^ 2 − x)$$

$$ x = (y^ 2 − y )\cdot \ln(3 + y^ 2 − y)$$ Any suggestions? Thank you

Answer 1

Neither $h(x)=x\space ln(3+x)$ nor $f(x)=x^2-x$ are injective ($h(0)=h(-2$)= $f(0)=f(1)=0$ and infinitely many other examples).Hence there neither $h^{-1}$ nor $f^{-1}$