TS EAMCET · Maths · Functions
A function \(f: \mathbb{R} \rightarrow \mathbb{R}\) defined by \(f(x)=\left\{\begin{array}{c}2 x+3, x \leq \frac{4}{3} \\ -3 x^2+8 x, x>\frac{4}{3}\end{array}\right.\) is
- A One-one function
- B not onto
- C a bijective function
- D constant function
Answer & Solution
Correct Answer
(B) not onto
Step-by-step Solution
Detailed explanation
Range of \(f(x)\) for \(x \leq \frac{4}{3}\): \(f(\frac{4}{3}) = 2(\frac{4}{3})+3 = \frac{17}{3}\). Range is \((-\infty, \frac{17}{3}]\). Range of \(f(x)\) for \(x > \frac{4}{3}\): Vertex of \(-3x^2+8x\) is at \(x = \frac{4}{3}\). Value at vertex is…
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