Question

(10.) Let f(x) be a function whose domain is (-5, 7] and g(x) = 12x + 5), then the domain of fog(x) is (A)(-5, 1] (B) (-4, 0] (C -6, 1] (D) none of these

JEE/Engineering Exams

Maths

Solution

4.0 (1 ratings)

[ begin{array}{l} text { Demain of } f(x)=[-5,7] g(x)=|2 x+5| end{array} ] Now, Demaing ( f(g(x)) ) must be such that the value given by ( g(x) ) is inside the domain of ( f(x) ) Hence, ( -5 leq|2 x+5| leq 7 ) But modelus values Earfi Can't be -ve. 2 [ begin{array}{l} therefore quad|2 x+5| leq 7 -7 leq 2 x+5 leq 7 -6 leq x leq 1 end{array} ] ( therefore ) the Pomain ( oint f(g(x)) ) is [-6,1] Answer