If `f(x) = (4a-7)/3 x^3+(a-3)x^2 +x+5` is one-one function find the range of a

Explanation

To determine the range of \( a \) for which the function

\[ f(x) = \frac{4a - 7}{3} x^3 + (a - 3)x^2 + x + 5 \]

is a one-one function, we need to analyze the derivative \( f'(x) \) and ensure it does not change sign (either always positive or always negative).

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