Let f: \mathbb{R} \rightarrow \mathbb{R} and g: \mathbb{R} \rightarrow \mathbb{R} be defined as:
f(x) = 2x + 3
g(x) = x^2 - 1
Which of the following statements is true ?

Question

Let   f: \mathbb{R} \rightarrow \mathbb{R}  and   g: \mathbb{R} \rightarrow \mathbb{R}  be defined as: 
  f(x) = 2x + 3 
  g(x) = x^2 - 1 
 Which of the following statements is  true ?

Answer

(f\circ g)(x) = 2x^2 + 1

Answer

(g\circ f)(x) = 2x^2 + 1

Answer

f^{-1}(x)  and   g^{-1}(x)  exist for all   x \in \mathbb{R} .

Answer

Neither   f^{-1}(x)  nor   g^{-1}(x)  exist for all   x \in \mathbb{R} .

Crowdly

Let f: \mathbb{R} \rightarrow \mathbb{R} and g: \mathbb{R} \rightarrow \m...

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