Question

[
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

# (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

Solution