AP EAMCET202022 Sep 2020Morning ShiftMathematicsFunctionsActual
Which of the following is true about f(x)=3 (x)-2 (x), x R
Options
- Af is an odd function
- Bf is a periodic function
- Cf is a strictly increasing function on R
- Df is a strictly decreasing function on R
Correct answer
C. f is a strictly increasing function on R
Step-by-step solution
Given, function, f(x)=3 h(x)-2 h(x) , x R aligned & =3 ( e^x-e^ -x 2 )-2 ( e^x+e^ -x 2 ) & = 1 2 e^x- 5 2 e^ -x = 1 2 (e^x-5 e^ -x ) f^ (x) & = 1 2 (e^x+5 e^ -x )>0 x R aligned The, function f is a strictly increasing function on R Hence, option (3) is correct.