(i) Find range of the function f(x)=15−cos 3x
(ii) If f(x)=√x2+1 and g(x)=2x2+3, find
(a) (f+g)(x) (b) f[g(x)]
(c) (f−g)x (d) (fg)(x)
(i) Given, f(x)=15−cos 3x
We know that, −1≤cos θ≤1
∴−1≤cos 3x≤1
⇒−1≤−cos 3x≤1
⇒−1+5≤5−cos 3x≤1+5
⇒4≤f(x)≤6
∴ Ranged of f(x)=[4,6]
(ii) Given , f(x)=√x2+1 and g(x)=2x2+3
(a) (f+g)(x)=f(x)+g(x)=√x2+1+2x2+3
(b) f[g(x)]=f(2x2+3)=√(2x2+3)2+1
=√4x4+9+12x2+1
=√4x4+12x2+10
(c) f−g)(x) =√x2+1−(2x2+3)=√x2+1−2x2−3
(d) (fg)x=f(x)g(x)=√x2+12x2+3