Find the range of f(x)=sin-1x+cos-1x+tan-1x
Find the range of the given function
Given: f(x)=sin-1x+cos-1x+tan-1x
Domain of sin-1x=-1,1
Domain of cos-1x=-1,1
Domain of tan-1x=-∞,∞
So f(x)=sin-1x+cos-1x+tan-1x is defined in -1,1
So, f(x)=π2+tan-1x[∵sin-1x+cos-1x=π2,x∈-1,1]
f'(x)=11+x2>0,∀x∈-1,1
Hencef(x) is an increasing function.
f(-1)=π2+tan(-1)=π2-π4=π4
f(+1)=π2+tan(+1)=π2+π4=3π4
Therefore, f(x)∈π4,3π4
Hence, the range of the given function is π4,3π4
Evaluate :cos48°-sin42°
Use the factor theorem to determine whether g(x) is a factor of f(x)
f(x)=22x2+5x+2;g(x)=x+2