If A is the domain and B is the range of the function f(x)= \ 3 x-1, x1 x^2+1, x ≤ 1 . then A-B=

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If A is the domain and B is the range of the function f(x)= \ 3 x-1, x>1 x^2+1, x ≤ 1 . then A-B=

MARKS Content Team · Accepted Answer

Correct answer: (B) (-∞, 1). ∵ f(x)= 3 x-1 x>1 x^2+1 x ≤ 1 ∴ Domain is (-∞, 1] ∪(1, ∞)=(-∞, ∞)=A When x>1 : f(x)=3 x-1 ⇒ 2 ≤ f(x) < ∞ and x ≤ 1: f(x)=x^2+1 ⇒ 1 ≤ f(x) < ∞ . ∴ Range B=(1, ∞) ∪(2, ∞)=[1, ∞) Now, A-B=(-∞, ∞)-[1, ∞)=(-∞, 1)

If $\mathrm{A}$ is the domain and $\mathrm{B}$ is the range of the function $f(x)=\left\{\begin{array}{ll}3 x-1, & x>1 \\ x^2+1, & x \leq 1\end{array}\right.$ then $A-B=$

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