Let f(x)= ln x and g(x)=(x4-2 x3+3 x2-2 x+2/2 x2-2 x+1). The domain of the composite function f ° g(x) is

Question

Let f(x)= ln x and g(x)=(x4-2 x3+3 x2-2 x+2/2 x2-2 x+1). The domain of the composite function f ° g(x) is (A) (-∞, ∞) (B) [0, ∞) (C) (0, ∞) (D) [1, ∞)

Tardigrade Admin · Accepted Answer

denominator ≠ 0 and numerator (x4+3 x2+2)-2 x(x2+1)=(x2+1)((x-1)2+1)

Q. Let $f (x) = ln x$ and $g (x) = \frac{x ^{4} - 2 x ^{3} + 3 x ^{2} - 2 x + 2}{2 x ^{2} - 2 x + 1}$ . The domain of the composite function $f \circ g (x)$ is

$(- \infty, \infty)$

$[0, \infty)$

$(0, \infty)$

$[1, \infty)$

denominator $\neq = 0$ and numerator $(x^{4} + 3 x^{2} + 2) - 2 x (x^{2} + 1) = (x^{2} + 1) ((x - 1)^{2} + 1)$

Q. Let f(x)=lnx and g(x)=2x2−2x+1x4−2x3+3x2−2x+2​. The domain of the composite function f∘g(x) is

(−∞,∞)

[0,∞)

(0,∞)

[1,∞)