Question

Let $f:[1,2]\to [1,4]andg:[1,2]\to [2,7]$ be two continuous bijective functions such that f(1) = 4 and g(2) = 7. Number of solution of the equation f(x) = g(x) in (1, 2) is equal to

• A. 1
• B. 2
• C. 3

Answer 1

The correct option is A 1

$f:[1,2]\to [1,4]g:[1,2]\to [2,7]f\left(1\right)=4g\left(2\right)=7$
$\because$ f(x) and g(x) are bijective functions f(x) is decreasing and g(x) is increasing functions.
$\therefore$ Two graphs will meet at only one point.