Question

Let $f:[1,2]\to [1,4]$ and $g:[1,2]\to [2,7]$ be two consecutive bijective functions such that $f\left(1\right)=4;g\left(2\right)=7$. The number of solutions of the equation $f\left(x\right)=g\left(x\right)$ in $(1,2)$ is

Answer 1

since $f\left(x\right)$ is bijective as well as $g\left(x\right)$and $f\left(1\right)=4$, so $f\left(x\right)$ is decreasing $g\left(2\right)=7$,so $g\left(x\right)$ is increasing.

Thus for$f\left(x\right)$$=g\left(x\right)$ in$(1,2)$ only one solution exist.