Mathematics - Definite Integration Question with Solution | TestHub

Let $f(\mathrm{x})={\int }_{-1}^{\mathrm{x}}{\mathrm{e}}^{{\mathrm{t}}^2}\mathrm{dt}$ and $\mathrm{h}(\mathrm{x})=\mathrm{f}(1+\mathrm{g}(\mathrm{x}))$, where $\mathrm{g}(\mathrm{x})$ is defined for all $\mathrm{x},{\mathrm{g}}^{\prime }(\mathrm{x})$ exists for all x , and $\mathrm{g}(\mathrm{x})<0$ for $\mathrm{x}>0$. If ${\mathrm{h}}^{\prime }(1)=\mathrm{e}$ and ${\mathrm{g}}^{\prime }(1)=1$, then the possible values which $\mathrm{g}(1)$ can take