If the functions f,g and h are defined from the set of real numbers ℝ→ℝ such that fx=x2-1, gx=x2+1 and hx=0,ifx<0x,ifx≥0 then h∘f∘gx is defined by
x
x2
0
None of these.
Explanation for the correct option:
The given functions are fx=x2-1, gx=x2+1 and hx=0,ifx<0x,ifx≥0.
Thus, h∘f∘gx=hfgx
⇒h∘f∘gx=hfx2+1[∵gx=x2+1]⇒h∘f∘gx=hx2+12-1[∵fx=x2-1]⇒h∘f∘gx=hx2+1-1⇒h∘f∘gx=hx2
As x2≥0, thus hx2=x2.
Therefore, h∘f∘gx=x2.
Hence, option(B) is the correct option
If f, g, h are real functions defined by f(x)=√x+1,g(x)=1x and h(x)=2x2−3, then find the values of (2f + g - h) (1) and (2f + g - h) (0).